Question

Find A if [413]A=[-484
-121
-363]=

Answer 1

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

To find : [A ]

Solution:

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

3 *  1     A   =    3  * 3

=> A  = 1  * 3  

$A = \left[\begin{array}{ccc}x&y&z\end{array}\right]$

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

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

=> x =  - 1   ,  y = 2   ,  z   =  1

$A = \left[\begin{array}{ccc}-1&2&1\end{array}\right]$

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