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  • Please Solve RD Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Very Short Asnwer Question 37 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Very Short Asnwer Question 37 Maths Textbook Solution.

Answers (1)

Answer:AA^{T}=\left [ 14 \right ]

Hint: Here, we use the basic transpose matrix concept

Given: A=\begin{bmatrix} 1 & 2 & 3 \end{bmatrix} with AA^{T}

Solution:

A=\begin{bmatrix} 1 & 2 & 3 \end{bmatrix}

A^{T}=\begin{bmatrix} 1\\ 2\\ 3 \end{bmatrix}\left [ For\: transpose \right ]

A\times A^{T}=\begin{bmatrix} 1\\ 2\\ 3 \end{bmatrix}\begin{bmatrix} 1 & 2 & 3 \end{bmatrix}

                 =\begin{bmatrix} 1 & 2 & 3 \end{bmatrix}_{1\times3} \begin{bmatrix} 1\\ 2\\ 3 \end{bmatrix}_{3\times1}

                 =Here both sides coloumn and row is similar.So,let's use matrix multiplication

                 = \left [ 1\times1+2\times2+3\times3 \right ]

                 = \left [ 1+4+9\right ]

 A\times A^{T}=\left [ 14 \right ]

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