RBSE Maths Class 12 Chapter 5: Inverse of a Matrix and Linear Equations Important Questions and Solutions

RBSE Class 12 Maths Chapter 5 – Inverse of a Matrix and Linear Equations Important questions and solutions are available here. All these important questions are given here and have detailed stepwise solutions.

## Table of Contents

Chapter 5 of RBSE Class 12 has only two exercises which cover various concepts of matrices such as singular, non-singular matrix, adjoint of a given matrix. Besides, different types of questions given here, such as finding the inverse of a matrix, finding the area of a triangle using determinant for the given vertices, solving a given system of equations using various methods involving matrix namely Cramer’s rule.

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- RBSE solution for Class 12 maths Chapter 5 | Inverse of a Matrix and Linear Equations solutions
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### RBSE Maths Chapter 5: Exercise 5.1 Textbook Important Questions and Solutions

**Question 1: For what value of x, is the matrix**

**[1−23121�2−3]****singular?**

**Solution:**

We know that if a matrix is singular, then its determinant is 0.

Thus,|1−23121�2−3|=0

⇒ 1 (-6 – 2) + 2 (-3 – x) + 3(2 – 2x) = 0

⇒ -8 – 6 – 2x + 6 – 6x = 0

⇒ -8x = 8

⇒ x = (-8/8) = -1

Therefore, the required value of x = -1.

**Question 2: If matrix A is**

**[1−1230−2103]****, then find adj A and prove that A.(adj A) = |A| I _{3} = (adj A).A.**

**Solution:**

Given matrix is:�=[1−1230−2103]

Cofactors of matrix A are:

Thus, the cofactor matrix of A=[0−11031−1283]

A.(adj A) = |A| I_{3} ….(i)

(adj A).A = |A| I_{3} ….(ii)

From (i) and (ii),

A.(adj A) = |A| I_{3} = (adj A).A.

Hence proved.

### RBSE Maths Chapter 5: Exercise 5.2 Textbook Important Questions and Solutions

**Question 3: Find the area of the triangle using the determinants whose vertices are (0, 0), (5, 0) and (3, 4).**

**Solution:**

Given,

Vertices of the triangle are (0, 0), (5, 0) and (3, 4).

Area of triangle=12|001501341|

= 1/2 [0(0 – 4) – 0(5 – 3) + 1(20 – 0)]

= 1/2(0 – 0 + 20)

= 20/2

= 10 sq.units

**Question 4: Solve the following system of equations using Cramer’s rule.**

**2x + 3y = 9**

**3x – 2y = 7**

**Solution:**

Given system of equations are:

2x + 3y = 9

3x – 2y = 7

Δ ≠ 0, Δ_{1} ≠ 0, Δ_{2} ≠ 0

Thus, the solution will be unique.

x = Δ_{1}/Δ = (-39)/(-13) = 3

y = Δ_{2}/Δ = (-13)/(-13) = 1

Therefore, the solution of the given system of equations is x = 3 and y = 1.

### RBSE Maths Chapter 5: Additional Important Questions and Solutions

**Question 1: If**

**�=[1−123]****, then find A ^{-1}.**

**Solution:**

Given,�=[1−123]

|A| = 3 – (-2) = 3 + 2 = 5

|A| ≠ 0

Thus, A-1 exists.

F11 = 3, F12 = -2, F21 = 1, F22 = 1

Cofactor matrix of A=[3−211]