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.

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

${\displaystyle }$

SOLUTION

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

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

∴ A^T = A i.e., A = A^T
∴ 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