Question

[2x 3]$\left[\begin{array}{cc}1& 2\\ -3& 0\end{array}\right]\left[\begin{array}{c}x\\ 3\end{array}\right]=0$ then find x.

Answer 1

We are given,

$\left[2x3\right]\left[\begin{array}{cc}1& 2\\ -3& 0\end{array}\right]\left[\begin{array}{c}x\\ 3\end{array}\right]=0$

We know that, $[aij{]}_{m\times n}$ can multiply with $[bij{]}_{n\times o}$ So we get a product as $[cij{]}_{m\times o}$ here $\left[cij\right]$ contains $[m\times o]$

entries.

So, $\left[2x3\right]1\times 2{\left[\begin{array}{cc}1& 2\\ -3& 0\end{array}\right]}_{2\times 2}{\left[\begin{array}{c}x\\ 3\end{array}\right]}_{2\times 1}$

$\left[2x\right(1)+3(-3\left)2x\right(2)+3(0){]}_{1\times 2}{\left[\begin{array}{c}x\\ 3\end{array}\right]}_{2\times 1}=0$

$[2x-94x]\left[\begin{array}{c}x\\ 3\end{array}\right]=0$

$(2x-9)\left(x\right)+\left(4x\right)\left(3\right)=0$

$2x^2-9x+12x=0$

$2x^2+3x=0$

$x(2x+3)=0$

So, $x=0$ or $2x+3=0$

$x=0$ or $x=\frac{-3}{2}$

The value of $x$ will be $0$ or $\frac{-3}{2}$