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MATRICES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMATRICES2 Marks
Question
Find x, y, z and t, if.
$3\begin{bmatrix}\text{x}&\text{y}\\\text{z}&\text{t}\end{bmatrix}=\begin{bmatrix}\text{x}&6\\-1&2\text{t}\end{bmatrix}+\begin{bmatrix}4&\text{x}+\text{y}\\\text{z}+\text{t}&3\end{bmatrix}$
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Answer

$3\begin{bmatrix}\text{x}&\text{y}\\\text{z}&\text{t}\end{bmatrix}=\begin{bmatrix}\text{x}&6\\-1&2\text{t}\end{bmatrix}+\begin{bmatrix}4&\text{x}+\text{y}\\\text{z}+\text{t}&3\end{bmatrix}$
$\Rightarrow\begin{bmatrix}3\text{x}&3\text{y}\\3\text{z}&3\text{t}\end{bmatrix}=\begin{bmatrix}\text{x}+4&6+\text{x}+\text{y}\\-1+\text{z}\text+{t}&2\text{t}+3\end{bmatrix}$
$\therefore\ 3\text{x}=\text{x}+4$
$\Rightarrow3\text{x}-\text{x}=4$
$\Rightarrow2\text{x}=4$
$\Rightarrow\text{x}=2$
Also,
$3\text{y}=6+\text{x}+\text{y}$
$\Rightarrow3\text{y}-\text{y}=6+\text{x}$
$\Rightarrow2\text{y}=6+\text{x}\ \dots(1)$
Putting the value of x in eq. (1), we get
$2\text{y}=6+2$
$\Rightarrow2\text{y}=8$
$\Rightarrow\text{y}=4$
Now,
$3\text{t}=2\text{t}+3$
$\Rightarrow3\text{t}-2\text{t}=3$
$\Rightarrow\text{t}=3$
$3\text{z}=-1+\text{z}+\text{t}$
$\Rightarrow3\text{z}-\text{z}=-1+\text{t}$
$\Rightarrow2\text{z}=-1+\text{t}\ \dots(2)$
Putting the value of t in eq. (2), we get
$2\text{z}=-1+3$
$\Rightarrow2\text{z}=2$
$\Rightarrow\text{z}=1$
$\therefore\ \text{x}=2,\text{ y}=4,\text{ z}=1$ and $\text{t}=3 $

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