NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.5

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NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.5 is provided in this article with step by step explanation. Chapter 4 Exercise 4.5 has questions covering concepts of determinants such as how to find the inverse of a matrix using adjoint. The questions make use of many theorems to deal with the adjoint and Inverse of a Matrix.

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Class 12 Maths Chapter 4 Determinants Topics:

Inverse Laplace Transform	Determinant Formula	Applications of determinants and matrices
Properties of Determinants	Determinants and Matrices	Elementary Matrix Operations
Difference between rows and columns	Jacobian Method	Consistent and inconsistent system of equations
Consistent System of Linear Equations	Minors and Cofactors	Non-singular matrix

CBSE Class 12 Mathematics Study Guides:

Math MCQs	Math Study Notes	Math Formula
Algebra	Geometry	Probability and Statistics
Calculus	Arithmetic	NCERT Solutions for Class 12 Maths
Mensuration	Trigonometry	Difference between in Maths

CBSE CLASS XII Related Questions

1.
Find the general solution of the differential equation \[ y\log y\,\frac{dx}{dy}+x=\frac{2}{y}. \]
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2.
If \[ P = \begin{bmatrix} 1 & -1 & 0 \\ 2 & 3 & 4 \\ 0 & 1 & 2 \end{bmatrix} \quad \text{and} \quad Q = \begin{bmatrix} 2 & 2 & -4 \\ -4 & 2 & -4 \\ 1 & -1 & 5 \end{bmatrix} \] find \( QP \) and hence solve the following system of equations using matrix method:
\[ x - y = 3,\quad 2x + 3y + 4z = 13,\quad y + 2z = 7 \]
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3.
A line passing through the points \(A(1,2,3)\) and \(B(6,8,11)\) intersects the line \[ \vec r = 4\hat i + \hat j + \lambda(6\hat i + 2\hat j + \hat k) \] Find the coordinates of the point of intersection. Hence write the equation of a line passing through the point of intersection and perpendicular to both the lines.
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4.
A rectangle of perimeter \(24\) cm is revolved along one of its sides to sweep out a cylinder of maximum volume. Find the dimensions of the rectangle.
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5.
Obtain the value of \[ \Delta = \begin{vmatrix} 1 + x & 1 & 1 \\ 1 & 1 + y & 1 \\ 1 & 1 & 1 + z \end{vmatrix} \] in terms of \(x, y, z\). Further, if \(\Delta = 0\) and \(x, y, z\) are non–zero real numbers, prove that \[ x^{-1} + y^{-1} + z^{-1} = -1 \]
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6.
Evaluate : \[ \int_{-\frac{\pi}{6}}^{\frac{\pi}{3}}(\sin|x|+\cos|x|)\,dx \]
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Similar Mathematics Concepts

Determinants: Types, Properties & Examples

Determinant of a Matrix: Definition, Calculation & Examples

Determinant: Formula, Properties and Applications

Consistent Systems of Linear Equations

NCERT Solutions for Class 12 Maths Chapter 4 Determinants

Determinants And Matrices: Definition, Types, Properties

Cayley Hamilton Theorem: Statement, Theorem, Proof & Sample Questions

Important Questions for Class 12 Math Chapter 4 Determinants

NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.1

NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.3

CBSE CLASS XII Previous Year Papers

Mathematics

Mathematics Preparation Guides

Matrices: Types, Properties, Formulas & Examples

Relations and Functions: Explanation, Types, and Representation

Types of Matrices: Row, Column, Zero, Symmetric, Skew Symmetric

Minors and Cofactors of Determinant: Definition, Formula and Solved Examples

Operations on Matrices: Addition, Subtraction, Multiplication and Solved Examples

Determinants: Types, Properties & Examples

Types of Relations: Definition, Classification and Examples

Properties of Determinants: Explanation, Important Properties and Examples

Plane: Equation of a Plane in Three-Dimensional Space

Invertible Matrices: Theorems, Properties and Examples

Symmetric and Skew Symmetric Matrices: Definition and Properties

Types of Functions: Elements, Equations, Range, and Domain

Introduction to Three-Dimensional Geometry: Distance, Important Formulae

Angle between Two Lines: Formula, Derivation & Calculation

Binary Operations: Types, Properties and Examples

Addition of Vectors: Definition, Formula, Laws and Properties

Types of Vectors: Definition, Properties & Examples

Definite Integral: Formula, Properties, Application & Examples

Integration by Partial Fractions: Formula, Steps & Examples

Angle Between a Line and a Plane: Formulas and Solved Examples

Mathematics NCERT Solutions

NCERT Solutions For Class 12 Mathematics Chapter 13: Probability

NCERT Solutions For Class 12 Mathematics Chapter 9: Differential Equations

NCERT Solutions For Class 12 Mathematics Chapter 7 Integrals

NCERT Solutions For Class 12 Mathematics Chapter 12: Linear Programming

NCERT Solutions for Class 12 Maths Chapter 3 Matrices

NCERT Solutions For Class 12 Mathematics Chapter 6 Applications of Derivatives

NCERT Solutions For Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions

NCERT Solutions for Class 12 Maths Chapter 4 Determinants

NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability

NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra

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