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Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMatrices2 Marks
Question
For what values of x: $\left[\begin{array}{lll}{1} & {2} & {1}\end{array}\right]$ $\left[\begin{array}{lll}{1} & {2} & {0} \\ {2} & {0} & {1} \\ {1} & {0} & {2}\end{array}\right]\left[\begin{array}{l}{0} \\ {2} \\ {x}\end{array}\right]$ = 0.
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Answer

$\left[\begin{array}{lll}{1} & {2} & {1}\end{array}\right]$ $\left[\begin{array}{lll}{1} & {2} & {0} \\ {2} & {0} & {1} \\ {1} & {0} & {2}\end{array}\right]\left[\begin{array}{l}{0} \\ {2} \\ {x}\end{array}\right]$ = O
$\Rightarrow$ $\left[\begin{array}{lll}{1+4+1} & {2+0+0} & {0+2+2}\end{array}\right]$ $\left[\begin{array}{l}{0} \\ {2} \\ {x}\end{array}\right]$ = O
$\Rightarrow$ $\left[\begin{array}{lll}{6} & {2} & {4}\end{array}\right]$ $\left[\begin{array}{l}{0} \\ {2} \\ {x}\end{array}\right]$ = O
$\Rightarrow$ [6(0) + 2(2) + 4(x)] = O
$\Rightarrow$ [4 + 4x] = [0]
$\therefore$ 4 + 4x = 0
$\Rightarrow$ x = -1.

Therefore,the required value of x is-1.

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