Question

Número 33 e 34, matriz ivertivel???

Answer 1

A matriz invertível tem determinante diferente de zero.

33)

$det~ \left[\begin{array}{cc}2&4\\-1&x\end{array}\right] \neq 0\\2*x-4*(-1) \neq 0\\2x+4 \neq 0\\2x\neq -4\\x\neq -4/2\\x \neq-2$
________________________

$det ~ \left[\begin{array}{ccc}a&1&1\\2&-1&1\\1&1&-3\end{array}\right]\neq 0$

$a*det~ \left[\begin{array}{cc}-1&1\\1&-3\end{array}\right]-2*det~\left[\begin{array} {cc}1&1\\1&-3\end{array}\right]+1*det~\left[\begin{array}{cc}1&1\\-1&1\end{array}\right]\neq 0$

$a*2-2*(-4)+1*2\neq 0\\2a+8+2\neq 0\\2a+10\neq 0 \\2a\neq -10\\a\neq-10/2\\a\neq5$