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Matrices — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSMatrices2 Marks
Question
Find X and Y, if $\mathrm{X}+\mathrm{Y}=\left[\begin{array}{ll} {7} & {0} \\ {2} & {5} \end{array}\right] \text { and } \mathrm{X}-\mathrm{Y}=\left[\begin{array}{ll} {3} & {0} \\ {0} & {3} \end{array}\right]$
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Answer

Given that, X + Y = $\left[\begin{array}{ll} {7} & {0} \\ {2} & {5} \end{array}\right]$ .....(1)
X - Y = $\left[\begin{array}{ll} {3} & {0} \\ {0} & {3} \end{array}\right]$ ....(2)
Adding (1) and (2), we get
$2 X=\left[\begin{array}{ll} {7} & {0} \\ {2} & {5} \end{array}\right]+\left[\begin{array}{ll} {3} & {0} \\ {0} & {3} \end{array}\right]$
$=\left[\begin{array}{ll} {7+3} & {0+0} \\ {2+0} & {5+3} \end{array}\right]$
 $=\left[\begin{array}{cc} {10} & {0} \\ {2} & {8} \end{array}\right]$
$\Rightarrow X=\frac{1}{2}\left[\begin{array}{ll} {10} & {0} \\ {2} & {8} \end{array}\right]=\left[\begin{array}{ll} {5} & {0} \\ {1} & {4} \end{array}\right]$
Now, X + Y =  $\left[\begin{array}{ll} {7} & {0} \\ {2} & {5} \end{array}\right]$
$\Rightarrow\left[\begin{array}{ll} {5} & {0} \\ {1} & {4} \end{array}\right]+Y=\left[\begin{array}{ll} {7} & {0} \\ {2} & {5} \end{array}\right]$
$\Rightarrow Y=\left[\begin{array}{ll} {7} & {0} \\ {2} & {5} \end{array}\right]-\left[\begin{array}{ll} {5} & {0} \\ {1} & {4} \end{array}\right]$
$\Rightarrow Y=\left[\begin{array}{ll} {2} & {0} \\ {1} & {1} \end{array}\right]$

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