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MATRICES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMATRICES5 Marks
Question
Find matrix A such that
$\begin{bmatrix} 2& -1\$0.3em] 1 & 0 \$0.3em] -3 & 4 \end{bmatrix}\text{A}=\begin{bmatrix} -1& -8\$0.3em] 1 & -2 \$0.3em] 9 & 22 \end{bmatrix}$
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Answer

Let $\begin{bmatrix} 2& -1 \$0.3em] 1 &1 \$0.3em] -3 & 4 \end{bmatrix}\begin{bmatrix} \text{a}& \text{b}\$0.3em] \text{c} &\text{d} \$0.3em] \end{bmatrix}=\begin{bmatrix} -1& -8 \$0.3em] 1 &-2 \$0.3em] 9 & 22 \end{bmatrix}$⇒$\begin{bmatrix} 2\text{a}-\text{c}& 2\text{b}-\text{d} \$0.3em] \text{a} &\text{b} \$0.3em] -3\text{a}+4\text{c} & -3\text{b} +4\text{d} \end{bmatrix}=\begin{bmatrix} -1&-8 \$0.3em] 1 &-2 \$0.3em] 9 & 22 \end{bmatrix}$
⇒ 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 $\therefore\ \text{A}=\begin{bmatrix} 1& -2 \$0.3em] 3&4 \$0.3em] \end{bmatrix}$

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