### For each of the following matrices, find its transpose and state whether it is symmetric, skew- symmetric or neither. [12-52-34-549]

Exercise 2.2 | Q 9.1 | Page 47

#### QUESTION

For each of the following matrices, find its transpose and state whether it is symmetric, skew- symmetric or neither.

$\left[\begin{array}{ccc}1& 2& -5\\ 2& -3& 4\\ -5& 4& 9\end{array}\right]$



#### SOLUTION

Let A = $\left[\begin{array}{ccc}1& 2& -5\\ 2& -3& 4\\ -5& 4& 9\end{array}\right]$

∴ AT = $\left[\begin{array}{ccc}1& 2& -5\\ 2& -3& 4\\ -5& 4& 9\end{array}\right]$

∴ AT = A i.e., A = AT
∴ A is a symmetric matrix.

Concept: Algebra of Matrices

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board

Chapter 2 Matrices

Exercise 2.2 | Q 9.1 | Page 47