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# Find A, if

Question:

Find A, if

Solution:

Given, $\left[\begin{array}{l}4 \\ 1 \\ 3\end{array}\right] A=\left[\begin{array}{rrr}-4 & 8 & 4 \\ -1 & 2 & 1 \\ -3 & 6 & 3\end{array}\right]$

Now, let $A=\left[\begin{array}{lll}x & y & z\end{array}\right]$

So, $\quad\left[\begin{array}{l}4 \\ 1 \\ 3\end{array}\right][x y z]=\left[\begin{array}{lll}-4 & 8 & 4 \\ -1 & 2 & 1 \\ -3 & 6 & 3\end{array}\right]$

$\Rightarrow\left[\begin{array}{ccc}4 x & 4 y & 4 z \\ x & y & z \\ 3 x & 3 y & 3 z\end{array}\right]=\left[\begin{array}{ccc}-4 & 8 & 4 \\ -1 & 2 & 1 \\ -3 & 6 & 3\end{array}\right]$

On comparing elements of both sides, we have

4x = -4 ⇒x = -1

4y = 8 ⇒ y = 2

And, 4z = 4 ⇒ z = 1

Therefore, A = [-1 2 1]

$A=\left[\begin{array}{cc}3 & -4 \\ 1 & 1 \\ 2 & 0\end{array}\right]$ and $B=\left[\begin{array}{lll}2 & 1 & 2 \\ 1 & 2 & 4\end{array}\right]$