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Matrices — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSMatrices1 Mark
Question
Assertion (A) : If $\left[\begin{array}{cc}x y & 4 \\ z+5 & x+y\end{array}\right]=\left[\begin{array}{cc}4 & w \\ 0 & 4\end{array}\right]$, then $x=2, y=2, z=-5$ and $w=4$.
Reason (R) : Two matrices are equal, if their orders are same and their corresponding elements are equal.
✓

Answer

(a) : $\left[\begin{array}{cc}x y & 4 \\ z+5 & x+y\end{array}\right]=\left[\begin{array}{cc}4 & w \\ 0 & 4\end{array}\right]$
On equating the corresponding elements, we get
$
x y=4, w=4, z+5=0 \text { and } x+y=4
$
On solving these equations, we get $x=2, y=2, z=-5$ and $w=4$. Also, the two matrices are equal, if their orders are same and their corresponding elements are equal.

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