Question

Calcule o determinante das matrizes

Answer 1

Olá




Por sarrus

A)



$\mathsf{ A=\left[\begin{array}{ccc}2&-1&4\\3&0&-2\\5&2&-1\end{array}\right] }\\\\\\\\\mathsf{A=\left|\begin{array}{cccc} 2 ~ ~~~~ ~~ & -1~ ~~~~ ~~ & 4~ ~~~~ ~ & 2 ~~ ~~-1\\ 3~ ~~~~ ~~ & 0~ ~~~~ ~~ & -2~ ~~~~ ~~ & 3~ ~~~~ ~~ 0 \\ 5 ~ ~~~~ ~~ & 2~ ~~~~ ~~ & -1 ~ ~~~~ ~~ & 5 ~ ~~~~ ~~2 \end{array}\right|}$


$\mathsf{\mathsf{\underbrace{(\mathsf{2\cdot0\cdot(-1)~+~(-1)\cdot(-2)\cdpt 5~+~4\cdot3\cdot2})}_{diag.~principal}}}\\\\\\\underbrace{(\mathsf{-1\cdot3\cdot(-1~)~+~2\cdot(-2)\cdot 2~+~4\cdot0\cdot5})}_{\mathsf{diag.~secund\'aria}}}}}\\\\\\\\\mathsf{=(0+10+24)~-~(3-8+0)}\\\\\\\mathsf{=34+5}\\\\\\\boxed{\mathsf{=39}}$




B)


$\displaystyle \mathsf{B= \left|\begin{array}{ccc} \frac{1}{2} &5\\\\-2&-8\\\end{array}\right| }\\\\\\\\\mathsf{=\underbrace{\left(\mathsf{ \frac{1}{2} \cdot(-8)}\right)}_{diag.~principal}~-\underbrace{(\mathsf{5\cdot(-2)})}_{diag.~secund\'aria}}\\\\\\\mathsf{=-4~-~(-10)}\\\\\\\boxed{\mathsf{=6}}$