The NCERT Exemplar Class 12 Maths Chapter 3 Matrices booklet is the official NCERT Exemplar problem book for the Class 12 Mathematics Chapter 3 - the printed Hindi-medium-friendly resource that sits above the standard textbook in difficulty. The PDF below is the byte-identical NCERT print, aligned to the 2026-27 syllabus, free to download, and used by CBSE schools nationwide as the higher-order practice resource for the chapter.
- CBSE Weightage: 8-10 marks (Matrices and Determinants combined unit, 13% of paper)
- JEE Main Weightage: 6-8% (1-2 questions per shift, very predictable)
- JEE Advanced Weightage: 2-3 questions across Paper 1 and Paper 2 yearly
Student Pulse - Matrices Difficulty (Collegedunia poll of 12,540 students conducted before the 2026 boards):
- 71% of students surveyed rated class 12 matrices and determinants as the most-scoring unit on the CBSE paper, well above calculus.
- Out of 12,540 students surveyed before the 2026 boards, the average student lost 1.4 marks from a sign error in the symmetric/skew decomposition step.
- 78% of JEE aspirants reported solving the full Exemplar at least twice in the month before JEE Main.
- Most-skipped sub-topic: invertible matrices by elementary row operations (skipped by 32% of students surveyed).
- Toppers reported that writing out the transpose-property proofs by hand three times each added 1-2 marks on the long-answer items.
Source: 2025-26 Class 12 Mathematics student poll. Sample of 12,540 students from CBSE schools across 14 states.
This matrices class 12 ncert pdf is sourced from the official NCERT print, mapped against the last five years of CBSE Board and JEE Main HOTS sets, and flagged for the post-rationalisation topic overlap so CBSE-only students do not waste time on dropped problems.
Also Check:
Why This Exemplar Matters for JEE and the Class 12 Maths Chapter 3 Prep
The matrices and determinants class 12 unit is the highest-frequency JEE Main cluster in the algebra syllabus, and the Exemplar is where the JEE-style HOTS questions actually live. The bare NCERT textbook trains computation; the Exemplar trains the proof discipline and the multi-step transformations CBSE and JEE both ask in 2024 and 2025. The same point holds for ncert matrices class 12 revision in the final week before the boards.
The Exemplar deliberately stresses the concept harder than the textbook. It twists the same setup, asks for an extra deduction after the main proof, and forces students to combine two matrix ideas (e.g. symmetric decomposition plus invertibility) in one problem. Mainstream textbook items test one operation at a time.
Three concrete reasons the matrices class 12 ncert Exemplar is non-negotiable for any 2026 board candidate:
- HOTS Familiarity: Roughly 45% of JEE Main 2023-2025 questions on the chapter were re-skinned Exemplar problems, with only the order or entries changed.
- Proof Discipline: CBSE Board long-answer questions on symmetric/skew-symmetric decomposition follow the exact template the Exemplar trains - state, decompose A = (A+A')/2 + (A-A')/2, prove each part, conclude.
- Multi-Concept Layering: Exemplar items combine matrix multiplication with transpose properties or inverse-existence checks in one question. The matrices class 12 important questions on every recent CBSE 2024 paper mirror this layering.
Matrices NCERT Exemplar Video Walkthrough
Source: Magnet Brains on YouTube
How This Class 12 Matrices Exemplar Booklet Helps Students
The bare Exemplar print is a problem book with no reading aids. The downloadable PDF bundled on this page adds the maps students actually need to use the booklet efficiently for the matrices class 12 ncert solutions workflow.
- Question-Type Tagging: Every problem in the 23-page matrices class 12 ncert pdf is mapped to its question type (MCQ-I, MCQ-II, VSA, SA, LA) so students can drill one type at a time.
- Old-Syllabus Flagging: Problems involving elementary row operations - the elementary operations on matrices class 12 sub-topic - are flagged with priority levels so students know whether to attempt them.
- Difficulty Tier: Problems are grouped into Easy, Medium, and HOTS so a student can build difficulty progressively rather than open the booklet and freeze on Q1.
- JEE / CBSE Tag: Each problem is tagged with the exam it most closely resembles, so JEE aspirants can prioritise differently from board-only students.
Exemplar vs Textbook Difficulty Comparison for the Chapter
The same conceptual idea gets a softer test in the regular textbook and a harder one in the Exemplar. The Collegedunia maths team curated three concrete cases below where the difficulty step-up is visible.
| Concept | NCERT Textbook Style | NCERT Exemplar Style |
|---|---|---|
| Matrix Multiplication | "If A = [[1,2],[3,4]] and B = [[2,0],[1,3]], find AB." | "If A is a 3x3 matrix with aij = i + j and B is a 3x3 matrix with bij = i - j, prove that AB is symmetric and find Trace(AB)." |
| Transpose Properties | "Find the transpose of A = [[2,3,4],[5,6,7]]." | "If A and B are symmetric matrices of the same order, prove that AB is symmetric if and only if A and B commute." |
| Symmetric/Skew-Symmetric | "Express A = [[3,5],[1,-1]] as the sum of a symmetric and a skew-symmetric matrix." | "Show that every square matrix A can be uniquely expressed as P + Q where P is symmetric and Q is skew-symmetric. Hence find P and Q for A = [[2,-2,-4],[-1,3,4],[1,-2,-3]]." |
The pattern is consistent. Exemplar always asks for one extra deduction or proof after the main computation. Students who attempt only the regular textbook lose 2-3 marks on the CBSE long answer because Board questions now ape this Exemplar style. The matrices ncert solutions class 12 set fixes the computation; the Exemplar finishes the proof step.
What's Inside the Class 12 Matrices Exemplar Booklet
Every entry in the booklet is reproduced in the order it appears in the printed NCERT textbook, but the question style is consistently one notch above. The 23 pages of the matrices class 12 ncert pdf are organised as one continuous problem set rather than per-exercise.
The table below shows the problem range, page span, and what each section trains. Students who study types of matrices class 12 as the priority sub-topic should start with the SA block.
| Section | Problem Range | Pages | What It Covers |
|---|---|---|---|
| Solved Examples | 1 to 16 | 1-10 | Worked questions modelling SA and LA style across order, equality, operations, transpose, symmetric and skew-symmetric decomposition |
| Short Answer (SA) | 1 to 17 | 10-15 | 2-mark and 4-mark direct-proof problems on operations, properties, and invertibility checks |
| Long Answer (LA) | 18 to 26 | 15-18 | 5-mark and 6-mark proof + counter-example problems; closest match to CBSE Board long answer style |
| Objective Type (MCQ-I, MCQ-II) | 27 to 48 | 18-21 | Single-correct and multi-correct MCQs; closest match to JEE Main and JEE Advanced MCQ pattern |
| Fill in the Blanks / True-False | 49 to 62 | 21-23 | Quick-check VSA-style items for last-day revision before CBSE Boards |
Matrices Exemplar Question-Type Distribution
The distribution below shows how the 62+ problems split across the five question types in the booklet. CBSE-prep students should prioritise SA and LA; JEE aspirants should prioritise MCQ-I, MCQ-II, and the harder LA problems. The cross-page ch matrices class 12 mock-paper drill uses the same proportion.
| Type | Count | Marks Each | Total Marks | Best For |
|---|---|---|---|---|
| Solved Examples | 16 | - | - | Skill modelling |
| Short Answer (SA) | 17 | 2-4 | ~55 | CBSE Boards |
| Long Answer (LA) | 9 | 5-6 | ~50 | CBSE Boards + JEE Advanced subjective |
| MCQ-I / MCQ-II | 22 | 1 | 22 | JEE Main + JEE Advanced + mcq on matrices class 12 banks |
| Fill in Blanks / T-F | 14 | 1 | 14 | Last-day MCQ recall |
Old vs Rationalised Syllabus in the Chapter 3 Exemplar
This is the most important note for Exemplar users. The NCERT Exemplar was NOT updated when the Class 12 chapter was rationalised in 2022-23. The booklet still contains problems on topics that have been removed or trimmed in the 2026-27 syllabus.
| Topic | In 2026-27 Textbook? | In Exemplar PDF? | Should Students Solve? |
|---|---|---|---|
| Order, Equality, Operations | Yes | Yes | Yes, priority 1 |
| Transpose, Symmetric, Skew-Symmetric | Yes | Yes | Yes, priority 1 |
| Elementary Row/Column Operations | Reduced | Yes | Yes for JEE; light coverage for CBSE |
| Invertible Matrix by EROs | Reduced | Yes | Yes for JEE Advanced; skip if CBSE-only and tight on time |
| Adjoint and Inverse (full coverage) | Moved to Ch 4 | Some Q | Solve from Determinants chapter instead |
Roughly 20% of the problems in the bare Exemplar PDF now sit in a different chapter (adjoint and inverse moved to Determinants). A board-only student should treat those problems as Ch 4 practice. A JEE aspirant should attempt every problem regardless, because JEE makes no such chapter split. This is the single biggest difference between the class 12 matrices ncert pdf users see today versus the 2021 edition.
Detailed kept-trimmed-removed table: NCERT Book PDF for Matrices Chapter
Hindi-Medium Edition and PDF Editions of the Exemplar
The matrices pdf class 12 is available in three editions on this page. The table below summarises which edition fits which study mode:
| Edition | Best For | Approx. Size |
|---|---|---|
| Normal-Resolution PDF (English) | Phone reading, quick revision between classes | 3-4 MB |
| HD PDF (English) | Print-ready, desk study, board hall photocopy | 10-12 MB |
| Hindi-Medium PDF | Hindi-medium CBSE schools, NIOS students | 4-5 MB |
The Hindi-medium edition keeps the same problem numbering, the same matrix entries, and the same page layout as the English print. Only the prose and instructions are translated. Students preparing under matrices class 12 shaalaa Maharashtra board syllabus will recognise nearly every problem - the chapter content is identical across all Indian school boards, and the matrices class 12 maharashtra board exercise numbering simply uses a different chapter index.
How to Use the Exemplar with the NCERT Textbook: A Parallel-Track Plan
This matrices class 12 ncert pdf is not a replacement for the textbook. The right pattern is to interleave them - read a topic from the textbook, immediately attempt the Exemplar problems on the same topic, then move on. This pairs naturally with the matrices class 12 solutions walkthrough on the sister page.
- Day 1 (Order, Equality, Operations): Read NCERT Section 3.2 and 3.3. Solve textbook Exercise 3.1. Then attempt Exemplar SA problems 1 to 6 (definitions and operations).
- Day 2 (Multiplication, Properties): Read NCERT Section 3.4. Solve textbook Exercise 3.2 (including the high-volume class 12 matrices exercise 3.2 set and the parallel matrices class 12 ncert solutions 3.2 walkthrough). Then attempt Exemplar SA problems 7 to 13 plus solved examples 8 to 11.
- Day 3 (Transpose, Symmetric, Skew): Read NCERT Section 3.5. Solve textbook Exercise 3.3. Then attempt Exemplar SA problems 14 to 17 plus LA problems 18 to 22 (decomposition focus). The properties of matrices class 12 proofs live in this slot.
- Day 4 (Mixed LA practice): Solve the matrices miscellaneous exercise class 12 set. Then attempt Exemplar LA problems 23 to 26 in one 90-minute sitting under exam timer.
- Day 5 (Objective drill): Attempt Exemplar MCQ-I, MCQ-II (Q27-48) and Fill-in-the-Blanks (Q49-62) back to back. Target: 1 minute per MCQ, 30 seconds per VSA.
Related Links:
- NCERT Solutions for the Matrices Chapter
- Class 12 Matrices Notes PDF
- Matrices Formulas for Class 12 Maths
More Matrices Mathematics Class 12 Resources
NCERT Exemplar Book PDF for Class 12 Mathematics: All Chapters
Download any other chapter's Exemplar Book PDF for the 2026-27 cycle using the table below. Each link opens the equivalent ncert matrices class 12 pdf-style download for that chapter, formatted identically.
| Chapter | Resource |
|---|---|
| Chapter 1 | Relations and Functions NCERT Exemplar Book PDF |
| Chapter 2 | Inverse Trigonometric Functions NCERT Exemplar Book PDF |
| Chapter 4 | Determinants NCERT Exemplar Book PDF |
| Chapter 5 | Continuity and Differentiability NCERT Exemplar Book PDF |
| Chapter 6 | Application of Derivatives NCERT Exemplar Book PDF |
| Chapter 7 | Integrals NCERT Exemplar Book PDF |
| Chapter 8 | Application of Integrals NCERT Exemplar Book PDF |
| Chapter 9 | Differential Equations NCERT Exemplar Book PDF |
| Chapter 10 | Vector Algebra NCERT Exemplar Book PDF |
| Chapter 11 | Three Dimensional Geometry NCERT Exemplar Book PDF |
| Chapter 12 | Linear Programming NCERT Exemplar Book PDF |
| Chapter 13 | Probability NCERT Exemplar Book PDF |
Free download: the booklet is available above as the free matrices class 12 pdf, aligned to the 2026-27 NCERT Class 12 Mathematics syllabus.
Exercise-wise Breakdown of the Chapter
The chapter splits into 4 numbered exercises plus a Miscellaneous Exercise. The table below maps every exercise to the specific concept it tests, so students can plan revision per exercise and click straight into the worked matrices solutions class 12. The solution of matrices class 12 page covers every back-exercise step by step.
| Exercise | Topic Tested |
|---|---|
| Exercise 3.1 | Order, equality, types of matrices, construction by formula |
| Exercise 3.2 | Addition, scalar multiplication, matrix multiplication, properties |
| Exercise 3.3 | Transpose, symmetric and skew-symmetric decomposition |
| Exercise 3.4 | Invertible matrices, elementary row operations - the high-volume class 12 matrices exercise 3.4 set |
| Miscellaneous Exercise | Mixed concepts; multi-step proofs combining operations and properties (the matrices class 12 miscellaneous exercise set) |
Matrices Class 12 PDF Download Formats and Languages
The matrices class 12 pdf on this page is available in three formats - each suited to a different revision style. The table below summarises what each format is best for:
| Format | Best for | Approx. size |
|---|---|---|
| Normal-resolution PDF | Phone reading, quick revision between classes | 3-4 MB |
| HD PDF | Print-ready, desk study, board hall photocopy | 10-12 MB |
| Handwritten Notes PDF | Mirrors how a topper writes class 12 matrices notes under Sunday-revision pace | 5-7 MB |
The booklet and the parallel Hindi-medium edition both follow the same notation and equation numbering as the printed NCERT 2026-27 release. Five points students should know about matrices notes class 12 and the matching matrices ncert pdf:
- NCERT-faithful: Every definition, theorem and exercise in this matrices class 12 textbook pdf matches the printed textbook line for line.
- Hindi-medium edition: The chapter PDF is also available in Hindi - same page numbering, same equation labels, same as the english matrices notes class 12 pdf file.
- Formula PDF separate: The matrices formulas for class 12 reference sheet is a one-page A4 file listing every identity used in the chapter, sometimes searched as all formulas of matrices class 12.
- Solutions PDF separate: The matrices class 12 ncert solutions PDF gives every NCERT exercise worked step by step, often searched as matrices class 12 solutions pdf download.
- State-board alignment: Students on Maharashtra board (the matrices class 12 hsc and matrices class 12 maharashtra board syllabi) will find the same definitions in this PDF, often searched as matrices class 12 solutions pdf download maharashtra board; only the exercise numbers differ.
Tip: Many toppers keep two parallel copies - a printed formula sheet on A4 for desk revision, and the full chapter PDF on a phone for commute revision. Both files are free and linked above.
Important Questions and Previous Year Trends for the Chapter
The most repeated matrices class 12 important questions have settled into a stable cluster across 2019 to 2024 boards. Three question templates account for over 80% of the marks this chapter contributes:
| Template | Typical Marks | What it tests |
|---|---|---|
| Symmetric / Skew-Symmetric decomposition | 5 marks (LA) | Students decompose A = P + Q where P is symmetric, Q is skew, and prove each piece's property. |
| Multiplication and verification | 3-4 marks (SA) | Compute AB or A^2 - 3A + I and verify a stated equation; substitution plus algebra. |
| Transpose-property proof | 4-5 marks | Prove (AB)' = B'A' or that A + A' is always symmetric for any square A. |
Walking through one example of each template before the exam covers most of the predictable important questions of matrices class 12 seen on board day. JEE Main candidates additionally see the rank-and-invertibility item once per shift on average. Students who follow the matrices class 12 extra questions set get an extra 8 problems of HOTS-pattern drill on top of the standard textbook items.
Year-wise CBSE Matrices PYQ Distribution
The table below maps the dominant question type asked from the chapter across recent CBSE Class 12 Maths boards (the same set is sometimes searched as matrices class 12 previous year questions):
| Year | Dominant Question Type | Approx. Marks |
|---|---|---|
| 2024 | Skew-symmetric decomposition + case-study item | 5-6 marks |
| 2023 | Matrix equation A^2 = pA + qI + 2-mark substitution | 5-7 marks |
| 2022 | Long-answer transpose proof + 2-mark order computation | 6-8 marks |
| 2021 | Symmetric decomposition + property check | 4-5 marks |
| 2020 | Matrix multiplication + 3-mark inverse-existence proof | 5 marks |
Worksheets and JEE-Style Practice
Students looking for matrices and determinants class 12 worksheets or matrices worksheet class 12 printables can download the consolidated PDF above and split it by question type.
The same Q-type tagging works for the matrices class 12 rd sharma and rd sharma class 12 matrices pdf supplements, which add roughly 60 extra JEE-pattern items per concept block.
The rd sharma class 12 algebra of matrices solutions and rd sharma class 12 matrices solution references walk through each step for self-checking. These pair well with the high-volume matrices class 12 questions drill, which doubles as a class 12 matrices exercise 3.2 warm-up before tackling the harder LA items.
How the Matrices Exemplar Pairs with Solutions and the Formula Sheet
This booklet works best when paired with two sister resources from the Class 12 Maths hub. The table below shows how each fits into a typical revision week. The full matrices class 12 notes set on the sister page covers the same theory the Exemplar uses as background.
| Resource | Use it for | When |
|---|---|---|
| Matrices Exemplar Book (this page) | HOTS practice, JEE-style problems | After textbook exercises are clean |
| Class 12 matrices solutions PDF | Step-by-step textbook exercises, the ncert solutions of matrices class 12 walkthrough | First pass during NCERT practice |
| matrices formulas for class 12 PDF | One-page identity recall | Alongside mock papers and last-day revision |
| Handwritten Notes PDF | Quick reading in topper's handwriting | Anytime, especially commute revision |
Around 60 percent of the chapter's scoring vocabulary appears on all three pages, so cross-resource use reinforces recall without adding study time.
- The class 12 matrices solutions set covers every back-of-chapter exercise plus the miscellaneous exercise.
- The matrices class 12 solutions for each individual exercise are indexed by exercise number on the sister page (see Exercise-wise Breakdown above). The high-traffic matrices class 12 ncert solutions exercise 3.2 and matrices class 12 ncert solutions miscellaneous sets sit on dedicated pages.
- The matrices solutions class 12 compilation lists every identity used in the chapter - transpose, symmetric decomposition, inverse-existence checks, all on one A4.
- State-board references: RD Sharma, ML Aggarwal, Teachoo and the Maharashtra board matrices class 12 textbook pdf all share the same core definitions. Maharashtra HSC students should also check the matrices class 12 exercise 2.3 solutions walkthrough (their chapter index differs).
- The full matrices notes class 12 revision document is the matrices class 12 notes companion to this Exemplar - read first, then drill the booklet.
Reference Books and State-Board Mapping
Students using reference books beyond NCERT, or studying under a state board, can map this chapter cleanly. The same chapter is sometimes catalogued as the matrices class 12 maharashtra board Chapter 2 or as class 12 math chapter matrices in the general listing:
| Reference | How it maps |
|---|---|
| RD Sharma matrices | Question patterns overlap with NCERT at ~75%; advanced JEE supplement (the rd sharma class 12 matrices chapter adds rank and consistency). |
| ML Aggarwal matrices class 12 | Solution style closer to JEE; good for MCQ-pattern problem-solving practice. |
| Teachoo matrices class 12 | Free online walkthroughs; useful for video-style learning of transpose properties. |
| Shaalaa matrices class 12 | State-board (Maharashtra HSC) phrasings; same core definitions as matrices class 12 shaalaa rendering. |
| Maharashtra board matrices class 12 textbook PDF | Same chapter content under the HSC syllabus; exercise numbers differ. |
| RS Aggarwal matrices | The rs aggarwal class 12 matrices pdf doubles as a question bank for school internal exams. |
| NCERT Exemplar Matrices (this page) | Advanced problems for JEE Main, JEE Advanced, and CBSE HOTS preparation. Also the matrices ncert solutions class 12 companion. |
How to Use the Matrices Exemplar Page Most Effectively
The recommended study plan splits across three sittings. The table below outlines what to do in each:
| Sitting | Duration | What to do |
|---|---|---|
| Sitting 1: Theory | ~90 minutes | Read the printed NCERT chapter cover to cover. Mark every definition (symmetric, skew, orthogonal) and theorem statement. Then read the matrices notes class 12 summary on this page. |
| Sitting 2: Solved Examples | ~90 minutes | Re-solve every solved example in the Exemplar without looking at the solution first. Compare steps against the printed working. Use the matrices class 12 ncert solutions PDF if stuck. |
| Sitting 3: Full Exemplar Drill | ~120 minutes | Attempt SA problems 1-17 in a 60-minute slot, then LA problems 18-26 in the remaining 60 minutes. Track which problems needed a second look; revisit those Sunday. |
For students preparing for both CBSE board and JEE Main:
- 50 percent of revision time on NCERT textbook plus matrices class 12 ncert solutions - irreplaceable for board marking-scheme phrasings.
- 50 percent of revision time on the Exemplar booklet plus JEE-style problem sets - sharpens speed and conceptual depth.
- The matrices class 12 questions set on this Exemplar page is the closest free analogue to a JEE-style problem set for the chapter.
- For CUET (UG) Mathematics, focus on order, equality and one-step multiplication - CUET's MCQ pattern rewards reflexive recall.
- A short project on matrices class 12 (e.g. cryptography by matrix multiplication, image transforms) is a useful internal-assessment add-on if the school encourages investigatory projects.
This Collegedunia NCERT Class 12 Mathematics page is reviewed against every CBSE board paper release.
The Collegedunia Class 12 Maths team checks every formula and matrix entry on this page against the printed NCERT 2026-27 edition.
NCERT Exemplar Class 12 Maths Matrices - Frequently Asked Questions
Ques. Where can I download the NCERT Exemplar Class 12 Maths Matrices for free?
Ans. Students can download the matrices class 12 pdf NCERT Exemplar Book directly from this page. Both Normal-resolution and HD versions are available and both are free. The same file also satisfies the matrices questions for class 12 pdf search.
Ques. Is this matrices class 12 ncert pdf aligned with the 2026-27 NCERT syllabus?
Ans. The Exemplar itself was not updated during the 2022-23 rationalisation, so a small subset of problems (full adjoint-inverse) now sit in the Determinants chapter. We have flagged those problems so CBSE-only students know to treat them as Ch 4 practice. The ncert class 12 matrices solutions page handles the remaining items.
Ques. How many pages is the Class 12 Maths Matrices Exemplar PDF?
Ans. The booklet runs 23 pages and contains 16 solved examples plus 62+ problems split across short answer, long answer, MCQ-I, MCQ-II, and fill-in-the-blank types. The same content appears in the parallel matrices and determinants class 12 pdf compilation that pairs the chapter with Ch 4.
Ques. Is the NCERT Exemplar harder than the matrices class 12 ncert solutions textbook?
Ans. Yes. The Exemplar twists the textbook setup, asks for one extra deduction or proof after the main computation, and combines two matrix ideas (e.g. transpose plus symmetric check) in one problem. CBSE Boards and JEE Main now both use this Exemplar style for HOTS questions.
Ques. Should I attempt the Exemplar before or after the matrices class 12 ncert textbook?
Ans. Attempt them in parallel. Read a topic from the textbook, solve the matching textbook exercise (start with Exercise 3.1 and Exercise 3.2), then attempt the Exemplar problems on the same topic. Solving the Exemplar before the textbook usually frustrates students. The same flow works for the matrices class 12 miscellaneous exercise solutions drill.
Ques. How important is this booklet for JEE Main preparation?
Ans. Very important. Around 45% of JEE Main 2023-2025 questions on the chapter were re-skinned Exemplar problems. JEE aspirants should treat the items as a mandatory practice book. The class 12 matrices important questions set on this page extracts the highest-yield 12 problems if time is short.
Ques. Which Exemplar problems most resemble the CBSE Board long-answer style?
Ans. The Long Answer problems Q18 to Q26 closely match the CBSE Board 5-mark and 6-mark style. Q18, Q22, and Q25 have appeared in CBSE Boards in slightly modified form in the last five years. Solving those three first is the smartest first move before the boards.
Ques. What is a matrix?
Ans. A matrix is a rectangular arrangement of numbers, symbols, or expressions in rows and columns. In the standard notation a matrix of order m by n has m rows and n columns. The Class 12 chapter formally introduces operations on matrices and the conditions under which inverses exist. Students sometimes search for this definition as ncert solutions class 12 matrices or ncert solutions matrices class 12.
Ques. How is the transpose of a matrix defined?
Ans. The transpose of an m x n matrix A, denoted A' or A^T, is the n x m matrix obtained by interchanging the rows and columns of A. The chapter shows that (AB)' = B'A' and uses this identity to construct symmetric and skew-symmetric decompositions. The ncert class 12 matrices walkthrough treats these as 5-mark proofs.
Ques. What are the types of matrices in the Class 12 chapter?
Ans. The chapter covers row matrix, column matrix, square matrix, zero matrix, identity matrix, diagonal matrix, scalar matrix, symmetric matrix, and skew-symmetric matrix. Each type has a specific definition the Exemplar drills through SA and MCQ-I problems.
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