Question

O determinante da matriz M= (1 4 0) (2 -1 1) (1 2 2) vale:?

Answer 1

Oi, Greissy! Tudo bem?

Façamos pelo método de Laplace:

$M= \left[\begin{array}{ccc}1&4&0\\2&-1&1\\1&2&2\end{array}\right] \\ \\ \\ det(M)= \left|\begin{array}{ccc}1&4&0\\2&-1&1\\1&2&2\end{array}\right| =\\ \\ \\1.(-1)^{3+1}\left|\begin{array}{cc}4&0\\-1&1\end{array}\right| + 2.(-1)^{3+2}\left|\begin{array}{cc}1&0\\2&1\end{array}\right| + 2.(-1)^{3+3}\left|\begin{array}{cc}1&4\\2&-1\end{array}\right| \\ \\ \\ =(4.1-(-1).0)-2(1.1-2.0)+2(1.(-1)-2.4)=4-2-18 \\ \\=-16$

Espero ter ajudado. Abraço!