For what values of x : [ lll 1 & 2 & 1 ] [ lll 1 & 2 & 0 2 & 0 & … - Vidyadip

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

$\left[\begin{array}{lll}{1} & {2} & {1}\end{array}\right] \left[\begin{array}{lll}{1} & {2} & {0} \\ {2} & {0} & {1} \\ {1} & {0} & {2}\end{array}\right] \left[\begin{array}{l}{0} \\ {2} \\ {x}\end{array}\right] = 0$
$\Rightarrow \left[\begin{array}{lll}{1+4+1} & {2+0+0} & {0+2+2}\end{array}\right] \left[\begin{array}{l}{0} \\ {2} \\ {x}\end{array}\right] = 0$
$\Rightarrow \left[\begin{array}{lll}{6} & {2} & {4}\end{array}\right] \left[\begin{array}{l}{0} \\ {2} \\ {x}\end{array}\right] = 0$
$\Rightarrow [6(0) + 2(2) + 4(x)] = 0$
$\Rightarrow [4 + 4x] = [0]$
$\therefore 4 + 4x = 0$
$\Rightarrow x = -1$.
Therefore,the required value of $x$ is $-1.$

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