para calcularmos det de ordem 2 basta multiplicarmos a diagonal principal e fazer a diferença com o produto da diagonal secundária (produto é o resultado da multiplicação:) super simples

OBS: na c está incorreto seria 2 - (-2) que daria 2+2 = 4 (:

Verified answer

Resposta:

a) Det = (-2)      c) Det = 4

b) Det = (-13)    d) Det = 6

e) Det = 1

Explicação passo a passo:

[tex]a)\ \left[\begin{array}{cc}1&2\\3&4\end{array}\right] \\\\\\Det=1\times4-2\times3\\\\Det=4-6\\\\Det=(-2)[/tex]

[tex]b)\ \left[\begin{array}{cc}2&9\\3&7\end{array}\right] \\\\\\Det=2\times7-9\times3\\\\Det=14-27\\\\Det=(-13)[/tex]

[tex]c)\ \left[\begin{array}{cc}1&-1\\2&2\end{array}\right] \\\\\\Det=1\times2-(-1)\times2\\\\Det=2+2\\\\Det=4[/tex]

[tex]d)\ \left[\begin{array}{cc}-2&4\\0&-3\end{array}\right] \\\\\\Det=(-2)\times(-3)-4\times0\\\\Det=6-0\\\\Det=6[/tex]

[tex]e)\ \left[\begin{array}{cc}\frac{1}{2} &\frac{1}{3} \\3&4\end{array}\right] \\\\\\Det=\frac{1}{2} \times4-\frac{1}{3} \times3\\\\Det=\frac{4}{2} -\frac{3}{3} \\\\Det=2-1\\\\Det=1[/tex]