Find the matrix A such that 4 1 3 A= -4&8&4 -1&2&1 -3&6&3 - Vidyadip

Question

Find the matrix A such that
$ \begin{bmatrix}4\\1\\3\end{bmatrix}\text{A}=\begin{bmatrix}-4&8&4\\-1&2&1\\-3&6&3\end{bmatrix}$

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Answer

Let $\text{A}=\begin{bmatrix}\text{x}&\text{y}&\text{z}\end{bmatrix}$
$\Rightarrow\begin{bmatrix}4\\1\\3\end{bmatrix}\begin{bmatrix}\text{x}&\text{y}&\text{z}\end{bmatrix}=\begin{bmatrix}-4&8&4\\-1&2&1\\-3&6&3\end{bmatrix}$
$\Rightarrow\begin{bmatrix}4\text{x}&4\text{y}&4\text{z}\\\text{x}&\text{y}&\text{z}\\3\text{x}&3\text{y}&3\text{z}\end{bmatrix}=\begin{bmatrix}-4&8&4\\-1&2&1\\-3&6&3\end{bmatrix}$
The corresponding elements of two equal matrices are equal.
⇒ 4x = -4 ...(1)
4y = 8 ...(2)
4z = 4 ...(3)
⇒ x = -1, y = 2 and z = 1
$\therefore\ \text{A}=\begin{bmatrix}-1&2&1\end{bmatrix}$

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