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MATRICES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMATRICES2 Marks
Question
If $\begin{bmatrix}\text{xy}&4\\\text{z}+6&\text{x}+\text{y}\end{bmatrix}=\begin{bmatrix}8&\text{w}\\0&6\end{bmatrix},$ then find the values of $x, y, z$ and $w$.
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Answer

$\begin{bmatrix}\text{xy}&4\\\text{z}+6&\text{x}+\text{y}\end{bmatrix}=\begin{bmatrix}8&\text{w}\\0&6\end{bmatrix}$
The corresponding entries of the two equal matrices are equal,
$\Rightarrow x y=8 \ldots(1)$
$w=4 \ldots(2)$
$z+6=0 \ldots(3)$
And $x+y=6 \ldots$ (4)
From equation (2) and equation (3) we get $z=-6$ and $w=4$.
From equation (4) we have,
$x+y=6$
$\Rightarrow x=6-y$,
Subsituting value of $x$ in equation (1) we get,
$\Rightarrow(6-y) y=8$
$\Rightarrow y^2-6 y+8=0$
$\Rightarrow(y-2)(y-4)=0$,
$\Rightarrow y=2,4$
Subsituting the value of $y$ in equation (1) we get,
$\Rightarrow x=4,2$
Therefore, value of $x, y, z, w$ are $2,4,-6,4$ or $4,2,-6,4$.

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