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 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| I3 = (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| I3 ….(i)
(adj A).A = |A| I3 ….(ii)
From (i) and (ii),
A.(adj A) = |A| I3 = (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, Δ1 ≠ 0, Δ2 ≠ 0
Thus, the solution will be unique.
x = Δ1/Δ = (-39)/(-13) = 3
y = Δ2/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]
