# NCERT solution class 12 chapter 3 Matrices exercise 3.3 mathematics part 1

## EXERCISE 3.3

#### Question 1:

Find the transpose of each of the following matrices:

(i) (ii) (iii) (i) (ii) (iii) #### Question 2:

If and , then verify that

(i) (ii) We have: (i) (ii) #### Question 3:

If and , then verify that

(i) (ii) (i) It is known that Therefore, we have: (ii) #### Question 4:

If and , then find We know that  #### Question 5:

For the matrices A and B, verify that (AB)′ = where

(i) (ii) (i) (ii) #### Question 6:

If (i) , then verify that (ii) , then verify that (i) (ii)  #### Question 7:

(i) Show that the matrix is a symmetric matrix

(ii) Show that the matrix is a skew symmetric matrix

(i) We have: Hence, A is a symmetric matrix.

(ii) We have: Hence, A is a skew-symmetric matrix.

#### Question 8:

For the matrix , verify that

(i) is a symmetric matrix

(ii) is a skew symmetric matrix (i)  Hence, is a symmetric matrix.

(ii)  Hence, is a skew-symmetric matrix.

#### Question 9:

Find and , when The given matrix is  #### Question 10:

Express the following matrices as the sum of a symmetric and a skew symmetric matrix:

(i) (ii) (iii) (iv) (i) Thus, is a symmetric matrix. Thus, is a skew-symmetric matrix.

Representing A as the sum of P and Q: (ii) Thus, is a symmetric matrix. Thus, is a skew-symmetric matrix.

Representing A as the sum of P and Q: (iii)  Thus, is a symmetric matrix. Thus, is a skew-symmetric matrix.

Representing A as the sum of P and Q: (iv) Thus, is a symmetric matrix. Thus, is a skew-symmetric matrix.

Representing A as the sum of P and Q: #### Question 11:

If AB are symmetric matrices of same order, then AB − BA is a

A. Skew symmetric matrix B. Symmetric matrix

C. Zero matrix D. Identity matrix

A and B are symmetric matrices, therefore, we have: Thus, (AB − BA) is a skew-symmetric matrix.

#### Question 12:

If , then , if the value of α is

A. B. C. π D.    