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Question
Find the matrix A such that `[[4],[1],[3]] A=[[-4,8,4],[-1,2,1],[-3,6,3]]`
Solution
\[\left( iii \right) \]
\[Let A = \begin{bmatrix}x & y & z\end{bmatrix}\]
\[ \Rightarrow \begin{bmatrix}4 \\ 1 \\ 3\end{bmatrix}\begin{bmatrix}x & y & z\end{bmatrix} = \begin{bmatrix}- 4 & 8 & 4 \\ - 1 & 2 & 1 \\ - 3 & 6 & 3\end{bmatrix}\]
\[ \Rightarrow \begin{bmatrix}4x & 4y & 4z \\ x & y & z \\ 3x & 3y & 3z\end{bmatrix} = \begin{bmatrix}- 4 & 8 & 4 \\ - 1 & 2 & 1 \\ - 3 & 6 & 3\end{bmatrix}\]
The corresponding elements of two equal matrices are equal .
\[ \Rightarrow 4x = - 4 . . . \left( 1 \right)\]
\[4y = 8 . . . \left( 2 \right) \]
\[4z = 4 . . . \left( 3 \right)\]
`⇒ x=-1,y=2, ` and `z=1`
\[ \therefore A = \begin{bmatrix}- 1 & 2 & 1\end{bmatrix}\]
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