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Matrices — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSMatrices1 Mark
Question
If $\left[\begin{array}{cc}2 a+b & a-2 b \\ 5 c-d & 4 c+3 d\end{array}\right]=\left[\begin{array}{cc}4 & -3 \\ 11 & 24\end{array}\right]$, then value of $a+b-c+2 d$ is
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Answer

From the definition of equality of two matrices, we have
$2 a+b=4 .... (i)$
$5 c-d=11 ..... (iii)$
$a-2 b=-3..... (ii)$
$4 c+3 d=24 ...... (iv)$
Solving $(i)$ and $(ii),$ we get
$5 a=5 $
$\Rightarrow a=1, b=2$
Solving $(iii)$ and $(iv),$ we get
$19 c=57$
$ \Rightarrow c=3, d=4$
$\therefore a+b-c+2 d=1+2-3+8=8$

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