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Choose the correct option.
If [2x 3] [1 2; -3 0] [x; 3] = O, then the values of x are:
If $\begin{bmatrix} 2x & 3 \end{bmatrix} \begin{bmatrix} 1 & 2 \\ -3 & 0 \end{bmatrix} \begin{bmatrix} x \\ 3 \end{bmatrix} = O$, then the values of $x$ are:
- a$0, -\frac{3}{2}$
- b$0, \frac{3}{2}$
- c$0, \frac{2}{3}$
- d$0, -\frac{2}{3}$
Answer
Answer
Correct option: a
Answer: (a) $0, -\frac{3}{2}$
$[2x\ \ 3]\begin{bmatrix}1&2\\-3&0\end{bmatrix}=[2x-9\ \ 4x]$, so the product with $\begin{bmatrix}x\\3\end{bmatrix}$ is $2x^2-9x+12x=2x^2+3x=x(2x+3)=0$, giving $x=0$ or $x=-\frac{3}{2}$.