# 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 = −X

^{T}So, A − A

^{T}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 = −X

^{T}Thus, A − A

^{T}is a skew-symmetric matrix.

**Question 3: **

**Solution:**

Given:

As we know that A = [a

_{ij}]_{m×n}is a symmetric matrix if a_{ij}= a_{ji}Thus,

x = a

_{13}= a_{31}= 4y = a

_{21}= a_{12}= 2z = a

_{22}= a_{22}= zt = a

_{32}= a_{23}= −3Hence, x = 4, y = 2, t = −3 and z can have any value.

**Questiion 4: **

**Solution:**

Given: