thetsanhtaroo thetsanhtaroo
  • 24-10-2020
  • Mathematics
contestada

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

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LammettHash
LammettHash LammettHash
  • 24-10-2020

I assume you're talking about two square matrices,

[tex]A=\begin{bmatrix}x^2&2\\x&1\end{bmatrix}[/tex]

and

[tex]B=\begin{bmatrix}x&2x\\3x&4x\end{bmatrix}[/tex]

If A is singular, then its determinant is 0:

[tex]\det A=x^2-2x=x(x-2)=0\implies x=0\text{ or }x=2[/tex]

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

[tex]\det B=4x^2-6x^2=-2x^2\neq0[/tex]

This tells you x ≠ 0, so x = 2.

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