Class 12 RD Sharma Solutions- Chapter 5 Algebra of Matrices – Exercise 5.5

Question 1:

Solution:

Given:

Consider,

From equation (1) and (2) it can be seen that,

A skew-symmetric matrix is a square matrix whose transpose equal to its negative, that is,

X = âˆ’XT

So, A âˆ’ AT is a skew-symmetric.

Question 2:

Solution:

Given:

Consider,

From equation (1) and (2) it can be seen,

A skew-symmetric matrix is a square matrix whose transpose equals its negative, that is,

X = âˆ’XT

Thus, A âˆ’ AT is a skew-symmetric matrix.

Question 3:

Solution:

Given:

As we know that A = [aij]mÃ—n is a symmetric matrix if aij = aji

Thus,

x = a13 = a31 = 4

y = a21 = a12 = 2

z = a22 = a22 = z

t = a32 = a23 = âˆ’3

Hence, x = 4, y = 2, t = âˆ’3 and z can have any value.

Question 4:

Solution:

Given:

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