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  • Explain Solution RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.5 Question 9 Maths.

Explain Solution RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.5 Question 9 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 &3 \\ 5& 7 \end{bmatrix}

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

A^{T} = \begin{bmatrix} 2 & 5\\ 3 &7 \end{bmatrix}

A + A^{T} = \begin{bmatrix} 2 &3 \\ 5& 7 \end{bmatrix}+\begin{bmatrix} 2 & 5\\ 3& 7 \end{bmatrix}

= \begin{bmatrix} 4 &8 \\ 8& 14 \end{bmatrix}

(A + A^{T})^{T} =\begin{bmatrix} 4 &8 \\ 8& 14 \end{bmatrix} = A + A^{T}

Hence,

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

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