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MATRICES — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSMATRICES5 Marks
Question
Find matrix A such that
$\begin{pmatrix} 2 & -1 \\ 1 & 0 \\ -3 & 4 \end{pmatrix}\text{A} = \begin{pmatrix} -1 & -8 \\ 1 & -2 \\ 9 & 22 \end{pmatrix}$
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Answer

$\text{Let} \begin{pmatrix} 2 & -1 \\ 1 & 0 \\ -3 & 4 \end{pmatrix}\begin{pmatrix} \text{a} & \text{b} \\ \text{c} & \text{d} \end{pmatrix} = \begin{pmatrix} -1 & -8 \\ 1 & -2 \\ 9 & 22 \end{pmatrix}$
$\Rightarrow \begin{pmatrix} \text{2a - c} & \text{2b - d} \\ \text{a} & \text{b} \\ \text{-3a + 4c} & \text{-3b + 4d} \end{pmatrix} = \begin{pmatrix} -1 & -8 \\ 1 & -2 \\ 9 & 22 \end{pmatrix}$
$\Rightarrow $ 2a – c = –1, 2b – d = –8
a = 1, b = –2
–3a + 4c = 9, –3b + 4d = 22
Solving to get a = 1, b = –2, c = 3, d = 4
$\therefore \text{A} = \begin{pmatrix} 1 & -2 \\ 3 & 4 \\ \end{pmatrix}$

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