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MATRICES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMATRICES5 Marks
Question
Find the matrix A such that $\begin{bmatrix}2&-1\\1&0\\-3&4\end{bmatrix}\text{A}=\begin{bmatrix}-1&-8&-10\\1&-2&-10\\9&22&15\end{bmatrix}.$
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Answer

We have, $\begin{bmatrix}2&-1\\1&0\\-3&4\end{bmatrix}_{3\times2}\text{A}=\begin{bmatrix}-1&-8&-10\\1&-2&-10\\9&22&15\end{bmatrix}_{3\times3}$ From the given equation, it is clear that order of A should be 2 × 3. Let $\text{A}=\begin{bmatrix}\text{a}&\text{b}&\text{c}\\\text{d}&\text{e}&\text{f}\end{bmatrix}$ $\therefore\ \begin{bmatrix}2&-1\\1&0\\-3&4\end{bmatrix}\begin{bmatrix}\text{a}&\text{b}&\text{c}\\\text{d}&\text{e}&\text{f}\end{bmatrix}=\begin{bmatrix}-1&-8&-10\\1&-2&-10\\9&22&15\end{bmatrix}$ $\Rightarrow\ \begin{bmatrix}2\text{a}-\text{d}&2\text{b}-\text{e}&2\text{c}-\text{f}\\\text{a}&\text{b}&\text{c}\\-3\text{a}+4\text{d}&-3\text{b}+4\text{e}&-3\text{c}+4\text{f}\end{bmatrix}=\begin{bmatrix}-1&-8&-10\\1&-2&-5\\9&22&15\end{bmatrix}$ By equality of matrices, we geta = 1, b = -2, c = -5
and 2a - d = -1 ⇒ d = 2a + 1 =3;
2b - e = -8 ⇒ e = 2(-2) + 8 = 4
2c - f = -10 ⇒ f = 2c + 10 = 0
$\therefore\ \text{A}=\begin{bmatrix}1&-2&-5\\3&4&0\end{bmatrix}$

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