NCERT Solutions for Maths Class 12 Exercise 3.3

Hello Students! In this post, you will find the complete NCERT Solutions for Maths Class 12 Exercise 3.3.

You can download the PDF of NCERT Books Maths Chapter 3 for your easy reference while studying NCERT Solutions for Maths Class 12 Exercise 3.3. 

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If you want to recall All Maths Formulas for Class 12, you can find it by clicking this link.

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NCERT Solutions for Maths Class 12 Exercise 3.1

NCERT Solutions for Maths Class 12 Exercise 3.2

NCERT Solutions for Maths Class 12 Exercise 3.4

NCERT Solutions for Maths Class 12 Exercise 3.3

Maths Class 12 Ex 3.3 Question 1.

Find the transpose of each of the following matrices:

Solution:

Maths Class 12 Ex 3.3 Question 2.

If  
then verify that:
(i) (A + B)’ = A’ + B’
(ii) (A – B)’ = A’ – B’

Solution:
We have,

Maths Class 12 Ex 3.3 Question 3.

If 
then verify that:
(i) (A + B)’ = A’ + B’
(ii) (A – B)’ = A’ – B’

Solution:

Maths Class 12 Ex 3.3 Question 4.

If 
then find (A + 2B)’

Solution:

We have,

Maths Class 12 Ex 3.3 Question 5.

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

Solution:

Maths Class 12 Ex 3.3 Question 6.

(i) If  , then verify that A’A = I

(ii) If  , then verify that A’A = I

Solution:

(i) We have,

Maths Class 12 Ex 3.3 Question 7.

(i) Show that the matrix  is a symmetric matrix.

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

Solution:
(i) For a symmetric matrix a_ij = a_ji
Now,

Here, a₁₂ = –1 = a₂₁, a₁₃ = 5 = a₃₁, a₂₃ = 1 = a₃₂

Again, a₁₁, a₂₂, a₃₃ are 1, 2, 3, respectively.

Hence, a_ij = a_ji

Therefore, A is a symmetric matrix.

Maths Class 12 Ex 3.3 Question 8.

For the matrix, , verify that

(i) (A + A’) is a symmetric matrix.
(ii) (A – A’) is a skew-symmetric matrix.

Solution:

We have,

Maths Class 12 Ex 3.3 Question 9.

Solution:

We have,

Maths Class 12 Ex 3.3 Question 10.

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

Solution:

Choose the correct answer in the following questions:

Maths Class 12 Ex 3.3 Question 11.

If A, B are symmetric matrices of same order, then AB – BA is a
(A) Skew symmetric matrix
(B) Symmetric matrix
(C) Zero matrix
(D) Identity matrix

Solution:
Since A and B are symmetric matrices, A’ = A and B’ = B.
Then, (AB – BA)’ = (AB)’ – (BA)’
= B’A’ – A’B’
= BA – AB
= –(AB – BA)
Therefore, AB – BA is a skew-symmetric matrix.

Hence, option (A) is correct.

Maths Class 12 Ex 3.3 Question 12.

If , then A + A’ = I, if the value of α is

(A) π/6            (B) π/3             (C) π             (D) 3π/2

Solution:
We have,

Hence, option (B) is correct.

Related Links:

NCERT Solutions for Maths Class 12 Exercise 3.1

NCERT Solutions for Maths Class 12 Exercise 3.2

NCERT Solutions for Maths Class 12 Exercise 3.4