Exercise 3.3 (Previous Year Question)

This sheet cover previous year questions based on exercise 3.2, chapter matrices, NCERT, Class 12 (Mathematics).

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Chapter: Matrices

Exercise – 3.3


 Transpose of a Matrix and Symmetric Matrix:-

 1 Mark Question:

1. If matrix A = [ ], then write AA’. [Delhi 2009;HOTS]
2. If A = *


+, the find A + A’, where A transpose of A. [All India 2009C]
3. If A = *


+, then find A + A’. [All India 2010C]
4. If

[



] and B = *


+ then find



. [All India 2012]
5. For what value of x, is a matrix A = [



] a skew symmetric matrix?
[All India 2013; HOTS]
6. Write 2 x 2 matrix which is both symmetric and skew symmetric matrices. [Delhi 2014C]
7. If (


), find α satisfying 0<α<π/2 when A+A
T
=√
; where A
T
is a transpose of
A. [All India 2016]
8. If the matrix [



] is skew symmetric, find the value of ‘a’ and ‘b’. [All India 2018]

 4 Mark Question:

9. For the following matrices a and b, verify that [AB]’ = B’A’; A =[



], B = [ ].
[All India 2010]
10. Express the following matrix as a sum of symmetric and skew-symmetric matrices and verify your
result. [



]. [All India 2010; HOTS]