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  • Explain Solution RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.5 Question 6 Maths.

Explain Solution RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.5 Question 6 Maths.

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Answer: A + A^{T}is a symmetric matrix.

Hint: FindA + A^{T}and prove that(A + A^{T}) = (A + A^{T})^{T}

Given:A = \begin{bmatrix} 2 &4 \\ 5 &6 \end{bmatrix}

Solution: A. is a symmetric matrix if and only ifA + A^{T} where AT is the transpose of matrix A.

AT = ^{T}= \begin{bmatrix} 2 &5 \\ 4 &6 \end{bmatrix}

A + A^{T} =\begin{bmatrix} 2 &4 \\ 5& 6 \end{bmatrix} + \begin{bmatrix} 2 & 5\\ 4& 6 \end{bmatrix}

= \begin{bmatrix} 4 &9 \\ 9& 12 \end{bmatrix}

(A + A^{T})^{T} =\begin{bmatrix} 4 &9 \\ 9 &12 \end{bmatrix}= A + A^{T}

Hence,

A + A^{T} is a symmetric matrix.

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