NCERT Solutions for Class 12 Maths Chapter 3 Matrices

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Class 12 Maths NCERT Solutions Chapter 3 Matrices is provided in the article below. A matrix is a rectangular grid in which numbers are arranged in rows and columns. There are many types of matrices and different operations that can be performed on them. Matrix is an important chapter in the Class 12 Maths Syllabus. The NCERT Solutions for Class 12 Mathematics Chapter 3 Matrices include concepts of types of matrices, operations on matrices, and symmetric and skew-symmetric matrices.

The chapter holds a weightage of about 10 marks in the CBSE Class 12 Examination along with the chapter Determinants. Generally, descriptive questions regarding solving for the values of x and y are asked from Matrices.

Download PDF: NCERT Solutions for Matrices

Class 12 Maths NCERT Solutions Chapter 3 Matrices

NCERT Solutions

Important Topics in Class 12 Mathematics Chapter 3 Matrices

Matrices is an important chapter of Class 12 Mathematics. The chapter covers topics of types of matrices, operations on matrices, symmetric and skew symmetric matrices, transpose of a matrix, elementary operation on matrix and invertible matrices. The main topics of the chapter include:

A matrix is a function consisting of an ordered rectangular array of numbers. If a matrix has m rows with n columns, then it is known as the matrix of order m x n.

The various types of matrices are Column matrix, Row matrix, Square matrix, Diagonal matrix, Scalar matrix, Identity matrix, and Zero matrix

If A = [a_ij] be a m x n matrix, then the matrix that is obtained by interchanging the rows and columns of A is known as the transpose of A and is denoted by A′ or (A^T).

For example, matrix A = \([ \begin{matrix} 2 &1 & 3 \\ -4 & 0 & 5 \\ \end{matrix} ]\),then transpose of A, (A^T) = \([ \begin{matrix} 2 & -4 \\ 1 & 0 \\ 3 & 5 \end{matrix} ]\)

A square matrix A = [a_ij] is symmetric matrix if the transpose of A is equal to A, i.e. [a_ij] = [a_ji] for all possible values of i and j.

A square matrix A = [aij] is said to be a skew-symmetric matrix if A′ = – A, that is a_ji= – a_ij for all possible values of i and j.

Invertible Matrix – If a square matrix A of order m, and another square matrix B of the same order m, satisfies AB = BA = I, then B is the inverse matrix of A, and is denoted by A^-1.

NCERT Solutions For Class 12 Maths Chapter 3 Exercises

The detailed solutions for all the NCERT Solutions for Matrices under different exercises are as follows:

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CBSE CLASS XII Related Questions

1.
A carpenter needs to design a wooden box in the shape of a cuboid such that the sum of its length and breadth is 3 cm more than its height. Twice of its length, thrice of its breadth and its height add up to 10 cm. Its breadth added to 7 times its height is 1 cm less than 3 times its length.
2.
Using integration, find the area of the region bounded by the curve \( y = x|x| \), the x-axis, and the vertical lines \( x = -2 \) and \( x = 2 \).
View Solution
3.
At a birthday party, children are being served orange juice in conical cups, as shown in the figure.

Each cup is 15 cm deep and has a radius 5 cm. The juice is being poured into this cup at a rate of 0·1 cm3/s.
On the basis of the above information, answer the following questions :
4.
Find the vector and cartesian equations of the line passing through the point of intersection of the lines \( \vec{r} = (\hat{i} + \hat{j} - \hat{k}) + \lambda(3\hat{i} - \hat{j}) \) and \( \vec{r} = (4\hat{i} - \hat{k}) + \mu(2\hat{i} + 3\hat{k}) \) and parallel to the line \( \frac{x - 1}{-2} = \frac{7 - y}{-3} = z \).
View Solution
5.
Find:

If the function \[ f(x)= \begin{cases} \frac{\sin x}{x}+\cos x, & x\neq0\\ k, & x=0 \end{cases} \] is continuous at \(x=0\), then find the value of \(k\).
- \(0\)
- \(-2\)
- \(-1\)
- \(2\)
View Solution
6.
An NGO organises a charity event in which they decide to distribute woollen caps to protect children from winter. The caps to be distributed are in three separate boxes, Box I has 30 red caps, Box II has 20 red and 10 green caps, and Box III has 30 green caps. The probability that a Box i is selected and a cap picked out is i/6, where i = 1, 2, 3.
Based on the above information, answer the following questions :