#### Need Solution for R .D. Sharma Maths Class 12 Chapter 4 Algebra of Matrices Exercise Multiple Choice Questions  Question 25 Maths Textbook Solution.

Answer: The correct option is (A).

$\frac{1}{2}\left(A+A^{\prime}\right)=\left[\begin{array}{ccc} 2 & 2 & -4 \\ 2 & 3 & 4 \\ -4 & 4 & 2 \end{array}\right]$

Given:$A=\left[\begin{array}{ccc} 2 & 0 & -3 \\ 4 & 3 & 1 \\ -5 & 7 & 2 \end{array}\right]$

Solution:

Then $A^{\prime}=\left[\begin{array}{ccc} 2 & 4 & -5 \\ 0 & 3 & 7 \\ -3 & 1 & 2 \end{array}\right]$

As the sum is expressed as,

\begin{aligned} B &=\frac{1}{2}\left(A+A^{\prime}\right) \\ &=\frac{1}{2}\left[\left[\begin{array}{ccc} 2 & 0 & -3 \\ 4 & 3 & 1 \\ -5 & 7 & 2 \end{array}\right]+\left[\begin{array}{ccc} 2 & 4 & -5 \\ 0 & 3 & 7 \\ -3 & 1 & 2 \end{array}\right]\right] \\ &=\frac{1}{2}\left[\begin{array}{ccc} 4 & 4 & -8 \\ 4 & 6 & 8 \\ -8 & 8 & 4 \end{array}\right] \\ &=\left[\begin{array}{ccc} 2 & 2 & -4 \\ 2 & 3 & 4 \\ -4 & 4 & 2 \end{array}\right] \end{aligned}

So, the correct option is (A).