# RBSE Solutions for Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

## Rajasthan Board RBSE Class 12 Maths Chapter 3 Matrix Miscellaneous Exercise

RBSE Solutions For Class 12 Maths Chapter 3 Miscellaneous Question 1. , then find A.
Solution:  RBSE Solutions For Class 12 Maths Chapter 3 Question 2. , then find (A – 2I) (A – 3I).
Solution: RBSE Solution Class 12 Maths Chapter 3 Question 3. , then find AB.
Solution: RBSE 12th Maths Chapter 3 Question 4. , then find BA.
Solution: RBSE Solutions For Class 10 Maths Chapter 3 Miscellaneous Question 5. , then find matrices A and B.
Solution:  Miscellaneous Exercise Chapter 3 Class 12 Question 6. , then find the value of x and y.
Solution:
On comparing,
x + 2 = -2 ∴ x = -4
– y – 2 = 5 ⇒ y = -7

Hence, x = -4, y = -7

Class 12 Maths Chapter 3 Miscellaneous Exercise Solutions Question 7.
Order of matrix A is 3 x 4 and B is a matrix, such that ATB and ABT defined, then write the order of B.
Solution:
∴ Order of A = 3 x 4
∴ Order of AT = 4 x 3
But ATB and ABT is defined.
So, order of B is 3 x 4.

Question 8. , is a symmetric matrix, then determine x.
Solution:
Given, On comparing aij = aji
a32 = a23 ⇒ -x = 4
∴ x = -4

RBSE Solutions For Class 12 Maths Chapter 3.2 Question 9.
Construct a matrix of order 3 x 3, B = [bij], whose elements are bij= (i) (j).
Solution:
B11 = 1 x 1 = 1
B12 = 1 x 2 = 2
B13 = 1 x 3 = 3

B21 = 2 x 1 = 2
B22 = 2 x 2 = 4
B23 = 2 x 3 = 6

B31 = 3 x 1 = 3
B32 = 3 x 2 = 6
B33 = 3 x 3 = 9 Miscellaneous Ex Ch 3 Class 12 Maths Question 10. Solution: Miscellaneous Exercise On Chapter 3 Class 12 Question 11.
Express matrix A as the sum of symmetric and skew-symmetric matrices, where .
Solution:
Given,  Class 12 Maths RBSE Solutions Question 12. then prove that :
(i) (AT)T = A
(ii) A + AT is a symmetric matrix.
(iii) A – AT is a skew-symmetric matrix.
(iv) AAT and ATA are symmetric matrix.
Solution:
(i) (AT)T = A (ii) A + AT is symmetric  So, A + AT is symmetric matrix. Hence Proved. So, A – AT is skew symmetric matrix. Proved.  Here,
a21 = a12 = 0
a31 = a13 = 0
a23 = a32 = 6
So, AAT is symmetric matrix. Here,
a12 = a21 = 0
a13 = a31 = 0
a32 = a23 = 4
So, ATA is symmetric matrix.

Chapter 3 Class 12 Maths Miscellaneous Question 13. , and 3A – 2B + C is a null matrix, then determine matrix ‘C’.
Solution:  Ex 3 Miscellaneous Class 12 Question 14.
Construct a matrix B = [bij] of the order 2 x 3, whose elements are bij = (i +2j)2/2
Solution:
Given, B = [bij] whose elements are RBSE Solutions For Class 12 Maths Question 15. , then find the element of 1st row of ABC.
Solution: So, element of 1st row is 8.

Class 12 Maths Ch 3 Miscellaneous Solutions Question 16. , then find AAT.
Solution:
Given, Miscellaneous Chapter 3 Class 12 Question 17. , then find x.
Solution:  Matrices Class 11 Solutions Question 18. , then prove Solution:
Given, = (bc – ad)I2 = R.H.S.
Hence Proved.

RBSE Solution Class 12 Maths Question 19. , then find the matrix form of the following (aA + bB) (aA – bB).
Solution:
Givn, RBSE Class 10 Maths Chapter 3 Miscellaneous Question 20. , then prove that (A – B)2 ≠ A2 – 2AB + B2.
Solution:
Given,   From (i) and (ii),
(A – B)2 + A2 – 2AB + B2
Hence Proved.

Class 12 Maths Ch 3 Miscellaneous Question 21. , then find k, where A2 = kA – 2IA2 .
Solution:
Given, On comparing corresponding element
From 3k – 2 = 1
3k = 3 ⇒ k = $$\frac { 3 }{ 3 }$$ ⇒ k = 1.

Matrices Class 12 Miscellaneous Exercise Solutions Question 22.
i = √-1 then prove that :
(1) A2 = B2 = C2 = -I2
(ii) AB = – BA = -C
Solution:   Miscellaneous Exercise On Chapter 3 Question 23. and f(A) = A2 – 5A + 7I then find f(A).
Solution: Miscellaneous Exercise Matrices Class 12 Question 24.
Prove that Solution:  