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Q12.    Given 3\begin{bmatrix}x & y \\ z & w \end{bmatrix} = \begin{bmatrix} x & 6 \\ -1 & 2w \end{bmatrix} + \begin{bmatrix} 4 &x + y \\ z + w & 3 \end{bmatrix}, find the values of x, y, z and w.

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3\begin{bmatrix}x & y \\ z & w \end{bmatrix} = \begin{bmatrix} x & 6 \\ -1 & 2w \end{bmatrix} + \begin{bmatrix} 4 &x + y \\ z + w & 3 \end{bmatrix}

\begin{bmatrix}3x &3 y \\3 z & 3w \end{bmatrix} = \begin{bmatrix} x+4 & 6+x+y \\ -1+z+w & 2w+3 \end{bmatrix}

If two matrices are equal than corresponding elements are also equal.

Thus, we have 

3x=x+4                                         

3x-x=4

2x=4

x=2

3y=6+x+y

Put the value of x

3y-y=6+2

2y=8

y=4

3w=2w+3

3w-2w=3

w=3

3z=-1+z+w

3z-z=-1+3

2z=2

z=1

Hence, we have x=2,y=4,z=1\, \, and\, \, w=3.

 

 

 

Posted by

seema garhwal

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