Question

If (x^2 2 x 1) is singular and (x 2x 3x 4x) is non-singular, find the value of x.

Answer 1

I assume you're talking about two square matrices,

`A=\begin{bmatrix}x^2&2\\x&1\end{bmatrix}`

and

`B=\begin{bmatrix}x&2x\\3x&4x\end{bmatrix}`

If A is singular, then its determinant is 0:

`\det A=x^2-2x=x(x-2)=0\implies x=0\text{ or }x=2`

B is not singular, so its determinant is not 0:

`\det B=4x^2-6x^2=-2x^2\\eq0`

This tells you x ≠ 0, so x = 2.