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  • Need solution for RD Sharma Maths Class 12 Chapter Algebra of Matrices Excercise 4.4 Question 1 Subquestion (iii).

Need solution for RD Sharma Maths Class 12 Chapter Algebra of Matrices Excercise 4.4 Question 1 Subquestion (iii).

Answers (1)

Answer: \left ( A-B \right )^{T}=A^{T}-B^{T}

Given:A=\begin{bmatrix} 2 &-3 \\ -7 &-5 \end{bmatrix}, B=\begin{bmatrix} 1 &0 \\ 2& -4 \end{bmatrix}

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

Solution:

                A^{T}=\begin{bmatrix} 2 &-7 \\ -3 &-5 \end{bmatrix}, B^{T}=\begin{bmatrix} 1 &2 \\ 0& -4 \end{bmatrix}

               \left ( A-B \right )^{T}=A^{T}-B^{T}

               \left ( \begin{bmatrix} 2 &-3 \\ -7 &5 \end{bmatrix}-\begin{bmatrix} 1 &0 \\ 2& -4 \end{bmatrix} \right )=\begin{bmatrix} 2 &-7 \\ -3 & 5 \end{bmatrix}-\begin{bmatrix} 1 &2 \\ 0&-4 \end{bmatrix}

                \begin{bmatrix} 1 &-3 \\ -9 &9 \end{bmatrix}^{T} =\begin{bmatrix} 1 &-9 \\ -3 & 9 \end{bmatrix}

                \begin{bmatrix} 1 &-9 \\ -3 &9 \end{bmatrix}^{T} =\begin{bmatrix} 1 &-9 \\ -3 & 9 \end{bmatrix}

∴ LHS=RHS

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