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  • Need solution for RD Sharma Maths Class 12 Chapter Algebra of Matrices Excercise 4.4 Question 2

Need solution for RD Sharma Maths Class 12 Chapter Algebra of Matrices Excercise 4.4 Question 2

Answers (1)

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

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

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

Solution:

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

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

    \left ( AB \right )^{T}=\begin{bmatrix} 3 &5 &5 \\ 0& 0 & 0\\ 12 & 20 & 8 \end{bmatrix}                                                                                      … (1)

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

                  =\begin{bmatrix} 3 &5 &2 \\ 0& 0 & 0\\ 12 & 20 & 8 \end{bmatrix}                                                                                              ….. (2)

(1) &( 2)

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

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