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please answer this question

in 2 min

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Answer 1

$\large\underline{\sf{Given \:Question - }}$

$\rm :\longmapsto\:3\bigg[ \begin{matrix}x&y \\ z&w \end{matrix} \bigg] = \bigg[ \begin{matrix}x&6 \\ - 1&2w \end{matrix} \bigg] + \bigg[ \begin{matrix}4&x + y \\ z + w&3 \end{matrix} \bigg]$

Find the values of x, y, z and w.

$\large\underline{\sf{Solution-}}$

Given matrix equation is

$\rm :\longmapsto\:3\bigg[ \begin{matrix}x&y \\ z&w \end{matrix} \bigg] = \bigg[ \begin{matrix}x&6 \\ - 1&2w \end{matrix} \bigg] + \bigg[ \begin{matrix}4&x + y \\ z + w&3 \end{matrix} \bigg]$

can be rewritten as

$\rm :\longmapsto\:\bigg[ \begin{matrix}3x&3y \\ 3z&3w \end{matrix} \bigg] = \bigg[ \begin{matrix}x + 4&6 + x + y \\ - 1 + z + w&2w + 3 \end{matrix} \bigg]$

So, on comparing, we get

$\red{\rm :\longmapsto\:3x = x + 4}$

$\red{\rm :\longmapsto\:3x - x = 4}$

$\red{\rm :\longmapsto\:2x = 4}$

$\red{\rm :\longmapsto\:x = 2}$

Also,

$\green{\rm :\longmapsto\:3y = 6 + x + y}$

$\green{\rm :\longmapsto\:3y - y= 6 + 2}$

$\green{\rm :\longmapsto\:2y= 8}$

$\green{\rm :\longmapsto\:y= 4}$

Also,

$\blue{\rm :\longmapsto\:3w = 2w + 3}$

$\blue{\rm :\longmapsto\:3w - 2w = 3}$

$\blue{\rm :\longmapsto\:w = 3}$

Also,

$\purple{\rm :\longmapsto\:3z = - 1 + z + w}$

$\purple{\rm :\longmapsto\:3z - z = - 1 + 3}$

$\purple{\rm :\longmapsto\:2z= 2}$

$\purple{\rm :\longmapsto\:z= 1}$

Answer 2

x=2

y=4

w=3

z=1

Explained in very brilliant manner in above.