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MATRICES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMATRICES3 Marks
Question
Find the matrix A such that
$\begin{bmatrix}2&-1\\1&0\\-3&4\end{bmatrix}\text{A}=\begin{bmatrix}-1&-8&-10\\1&-2&-5\\9&22&15\end{bmatrix}$
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Answer

Let $\text{A}=\begin{bmatrix}\text{x}&\text{y}&\text{z}\\\text{a}&\text{b}&\text{c}\end{bmatrix}$
$\Rightarrow\begin{bmatrix}2&-1\\1&0\\-3&4\end{bmatrix}\begin{bmatrix}\text{x}&\text{y}&\text{z}\\\text{a}&\text{b}&\text{c}\end{bmatrix}=\begin{bmatrix}-1&-8&-10\\1&-2&-5\\9&22&15\end{bmatrix}$
$\Rightarrow\begin{bmatrix}2\text{x}-\text{a}&2\text{y}-\text{b}&2\text{z}-\text{c}\\\text{x}&\text{y}&\text{z}\\-3\text{x}+4\text{a}&-3\text{y}+4\text{b}&-3\text{z}+4\text{c}\end{bmatrix}=\begin{bmatrix}-1&-8&-10\\1&-2&-5\\9&22&15\end{bmatrix}$
By comparing the elements of second row, we get
x = 1, y = -2 z = -5
By comparing the elements of first row, we get
2x - a = -1
⇒ 2 - a = -1
⇒ a = 3
Also,
2y - b = -8
⇒ -4 - b = -8
⇒ b = 4
And
2z - c = -10
⇒ -10 - c = -10
⇒ c = 10
$\therefore\ \text{A}=\begin{bmatrix}1&-2&-5\\3&4&0\end{bmatrix}$

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