## 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 – a^{2} – 8=0

⇒ a^{2} – 2a – 4a + 8 = 0

⇒ a^{2} – 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.