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  • Need solution for RD Sharma Maths Class 12 Chapter Algebra of Matrices Excercise 4.4 Question 5

Need solution for RD Sharma Maths Class 12 Chapter Algebra of Matrices Excercise 4.4 Question 5

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Answer: \left ( AB\right )^{T}=\begin{bmatrix} 0 &1 \\ 15 & -2 \end{bmatrix}

Given:A=\begin{bmatrix} 2 & 4 & -1\\ -1 &0 & 2 \end{bmatrix},B=\begin{bmatrix} 3 &4 \\ -1 &2 \\ 2 & 1 \end{bmatrix}

Hint: The  A^{T} of matrix A can be obtained by reflecting the elements along it’s main diagonal.

Solution:

               \left ( AB \right )=\begin{bmatrix} 2 & 4 &-1 \\ -1 & 0 & 2 \end{bmatrix}\begin{bmatrix} 3 & 4\\ -1 & 2\\ 2 & 1 \end{bmatrix}

                          =\begin{bmatrix} 6-4-2 & 8+8-1\\ -3-0+4 & -4+0+2 \end{bmatrix}

               \left [ AB \right ]=\begin{bmatrix} 0 & 15\\ 1 & -2 \end{bmatrix}

                \left [ AB \right ]^{T}=\begin{bmatrix} 0 & 1\\ 15 & -2 \end{bmatrix}

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