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

Question

asked Oct 16, 2021 198k views

1 Answer

Casonadams · Answer 1 · 2021-10-22T10:04:58+0000

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.