1. Tardigrade
  2. Question
  3. Mathematics
  4. The value of x such that [1 2 1][1 2 0 2 0 1 1 0 2][0 2 x]=O, is

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Q. The value of $x$ such that $\begin{bmatrix}1 & 2 & 1\end{bmatrix}\begin{bmatrix}1 & 2 & 0 \\ 2 & 0 & 1 \\ 1 & 0 & 2\end{bmatrix}\begin{bmatrix}0 \\ 2 \\ x\end{bmatrix}=O$, is

Matrices

Solution:

Given, $\begin{bmatrix}1 & 2 & 1\end{bmatrix}\left(\begin{bmatrix}1 & 2 & 0 \\ 2 & 0 & 1 \\ 1 & 0 & 2\end{bmatrix}\begin{bmatrix}0 \\ 2 \\ x\end{bmatrix}\right)=0$
$\rightarrow \begin{bmatrix}1 & 2 & 1\end{bmatrix}\begin{bmatrix}1 & 2 & 0 \\ 2 & 0 & 1 \\ 1 & 0 & 2\end{bmatrix}\begin{bmatrix}0 \\ 2 \\ x\end{bmatrix}=0$
$\rightarrow \begin{bmatrix}1 & 2 & 1\end{bmatrix}\begin{bmatrix}0+4+0 \\ 0+0+x \\ 0+0+2 x\end{bmatrix}=0$
( $\because$ matrix multiplication is associative)
$\rightarrow \begin{bmatrix}1 & 2 & 1\end{bmatrix}\begin{bmatrix}4 \\ x \\ 2 x\end{bmatrix}=0 \rightarrow[4+2 x+2 x]=0$
$\rightarrow 4+4 x=0 \rightarrow x=-1$