If \( \begin{bmatrix}2 & x & 3\end{bmatrix}\begin{bmatrix}-1 & 0 & -1\\-1 & 1 & 0\\0 & 1 & 1\end{bmatrix}\begin{bmatrix}x\\0\\-1\end{bmatrix}=[-4] \) , then the value (/s) of \( x \) is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( -3 \), 1
Multiplying the row matrix by the square matrix first:
\( \displaystyle \begin{bmatrix}2 & x & 3\end{bmatrix}\begin{bmatrix}-1 & 0 & -1\\-1 & 1 & 0\\0 & 1 & 1\end{bmatrix} \)
\( \displaystyle =\begin{bmatrix}-2-x & x+3 & -2+3\end{bmatrix} \)
\( \displaystyle =\begin{bmatrix}-2-x & x+3 & 1\end{bmatrix} \)
Then by the column matrix:
\( (-2-x)(x)+(x+3)(0)+(1)(-1)=-x^2-2x-1 \)
\( -x^2-2x-1=-4 \)
\( x^2+2x-3=0 \)
\( (x+3)(x-1)=0 \)
So x = −3 or x = 1.