NCERT Solutions for Class 12 Maths Chapter 3 Matrices Ex 3.3

In this chapter, we provide NCERT Solutions for Class 12 Maths Chapter 3 Matrices Ex 3.3 for English medium students, Which will very helpful for every student in their exams. Students can download the latest NCERT Solutions for Class 12 Maths Chapter 3 Matrices Ex 3.3 pdf, free NCERT solutions for Class 12 Maths Chapter 3 Matrices Ex 3.3 book pdf download.

Board	CBSE
Textbook	NCERT
Class	Class 12
Subject	Maths
Chapter	Chapter 3
Chapter Name	Matrices
Exercise	Ex 3.3
Number of Questions Solved	12
Category	NCERT Solutions

NCERT Solutions for Class 12 Maths Chapter 3 Matrices Ex 3.3

Ex 3.3 Class 12 Maths Question 1.
Find the transpose of each of the following matrices:
(i)
(ii)
(iii)
Solution:
(i) let A =
∴ transpose of A = A’ =

Ex 3.3 Class 12 Maths Question 2.
If
then verify that:
(i) (A+B)’=A’+B’
(ii) (A-B)’=A’-B’
Solution:

Ex 3.3 Class 12 Maths Question 3.
If
then verify that:
(i) (A+B)’ = A’+B’
(ii) (A-B)’ = A’-B’
Solution:

Ex 3.3 Class 12 Maths Question 4.
If
then find (A+2B)’
Solution:

Ex 3.3 Class 12 Maths Question 5.
For the matrices A and B, verify that (AB)’ = B’A’, where


Solution:

Ex 3.3 Class 12 Maths Question 6.
If (i) ,the verify that A’A=I
If (ii) ,the verify that A’A=I
Solution:
(i)

Ex 3.3 Class 12 Maths 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,

Ex 3.3 Class 12 Maths Question 8.
For the matrix,
(i) (A+A’) is a symmetric matrix.
(ii) (A-A’) is a skew-symmetric matrix.
Solution:

=>

Ex 3.3 Class 12 Maths Question 9.
Find and ,when

Solution:

Ex 3.3 Class 12 Maths Question 10.
Express the following matrices as the sum of a symmetric and a skew-symmetric matrix.
(i)
(ii)
(iii)
(iv)
Solution:
(i) let
=>

Ex 3.3 Class 12 Maths Question 11.
Choose the correct answer in the following questions:
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:
Now A’ = B, B’ = B
(AB-BA)’ = (AB)’-(BA)’
= B’A’ – A’B’
= BA-AB
= – (AB – BA)
AB – BA is a skew-symmetric matrix Hence, option (a) is correct.

Ex 3.3 Class 12 Maths Question 12.
If then A+A’ = I, if the
value of α is
(a)
(b)
(c) π
(d)
Solution:
Now

Thus option (b) is correct.

All Chapter NCERT Solutions For Class12 Maths

—————————————————————————–

All Subject NCERT Solutions For Class12

*************************************************

Remark:

I think you got complete solutions for this chapter. If You have any queries regarding this chapter, please comment on the below section our subject teacher will answer you. We tried our best to give complete solutions so you got good marks in your exam.

If these solutions have helped you, you can also share Careerkundali.in to your friends.

Best of Luck!!