RBSE Solutions for Class 12 Maths Chapter 3 Matrix Ex 3.1

Rajasthan Board RBSE Class 12 Maths Chapter 3 Matrix Ex 3.1

Question 1.
If A = [a_ij]_{2 x 4}, then write the number of elements in A.
Solution: 8

Question 2.
Write identity matrix of order 4 x 4.
Solution:
Unit matrix of 4 x 4

Question 3.
If , then find the value of a.
Solution:
Given,

∴ On comparing
∴ k +4 = a …….(i)
k – 6 = -4 …….(ii)
From (i),
k = -4 + 6 = 2
From (ii),
a = k + 4 = 6
∴ a = 6

Question 4.
What are the possible order of matrix, having 6 elements ?
Solution:
6 x 1, 1 x 6, 2 x 3 and 3 x 2.

Question 5.
Construct a 2 x 2 matrix A = [a_ij], where elements are given by :

Solution:

Question 6.
Construct a matrix A = [a_ij] of order 2 x 3, whose elements are a[a_ij] = \(\frac { 1 }{ 2 }\) | 2i – 3i| .
Solution:
In 2 x 3, there are 2 rows and 3 columns
So, i = 1, 2 and j = 1, 2, 3

Question 7.

then find ‘a’ and ‘b’.
Solution:

On comparing,
a + b = 6 ……(i)
ab = 8
From equation (i) and (ii),
a(6 – a)= 8
⇒ 6a – a² – 8=0
⇒ a² – 2a – 4a + 8 = 0
⇒ a² – 2a – 4a + 8 = 0
² (a – 2)(a – 4) = 0
So, a = 2, 4
From ab = 8 we get b = 4, 2

Question 8.
, then find the value of x, y, z and p.
Solution :

On comparing
2x = 4
⇒ x = 2
⇒ 3x + y = 5
y = 5 – 3 x 2 = 5 – 6 = -1
-x + z = -4
z = -4 + x = -4 + 2 = – 2
⇒ 3y – 2p = -3
⇒ 2p = 3y + 3 = 3 x -1 + 3 = 0
So, p = 0
x = 2, y = -1, z = -2, p = 0.

Question 9.
Find the values of a, b and c if matrices A and B are equal, where

Solution :
Given, A = B

On comparing
a – 2 = b
⇒ a – b = 2 …..(i)
3 = c
12c = 6b
⇒ b = \(\frac { 12 x 3 }{ 6 }\) = 6
⇒ b = 6
From b + 2 = a,
a – b = 2
∴ a = 2 + b = 2 + 6 = 8
So, a = 8, b = 6, c = 3.

RBSE Solutions for Class 12 Maths