**Chapter 4 Determinants and Matrices Ex 4.7**

## Chapter 4 Determinants and Matrices Ex 4.7

**Question 1.**

**Question 2.**

∴ = -A and A = –

∴ A and A

^{T}both are skew-symmetric matrices.

**Question 3.Solution:**

From (i) and (ii), we get

(2A = 2

**Question 4.Solution:**

From (i) and (ii), we get

(3A = 3

**Question 5.Solution:**

**Question 6.Solution:**

From (i) and (ii), we get

[Note: The question has been modified.]

From (i) and (ii), we get

**Question 7.Solution:**
3A – 2B + C = I

∴ C = I + 2B – 3A

**Question 8.Solution:**

**Question 9.Solution:**

A + 2B + 3C

**Question 10.Solution:**

From (i) and (ii), we get

**Question 11.Solution:**

**Question 12.Express the following matrices as the sum of a symmetric and a skew symmetric matrix.Solution:**

A square matrix A can be expressed as the sum of a symmetric and a skew symmetric matrix as

**Question 13.Solution:**

From (i) and (ii), we get

^{}

From (i) and (ii) we get

**Question 14.Solution:**

∴ A = I, where I is the unit matrix of order 2.