Question

Calcule os determinantes das matrizes abaixo:$a)\left[\begin{array}{cc}1&5\\-8&7\\\end{array}\right] \\\\b)\left[\begin{array}{cc}1000\end{array}\right] \\\\c)\left[\begin{array}{ccc}1&0&0\\47&7&-7\\1&4&10\end{array}\right] \\\\d)\left[\begin{array}{cc}1&1\\1&1\end{array}\right] \\\\e)\left[\begin{array}{cccc}1&2&4&2\\7&0&4&0\\-8&7&0&1\end{array}\right]$

Answer 1

a)

$\left[\begin{array}{cc}1&5\\-8&7\\\end{array}\right] \\ \\ det = 1.7 - 5.( - 8) \\ det =7 + 40 \\ det =47$

c)

$\left[\begin{array}{ccc}1&0&0\\47&7&-7\\1&4&10\end{array}\right] \\ \\ \\ 1 \times \left[\begin{array}{cc}7& - 7\\4&10\\\end{array}\right] - 0 \times \left[\begin{array}{cc}47& - 7\\1&10\\\end{array}\right] + 0 \times \left[\begin{array}{cc}47&7\\1&4\\\end{array}\right] \\ \\ 98 + 0 + 0 \\ 98$

d)

$\left[\begin{array}{cc}1&1\\1&1\end{array}\right] \\ \\ det = 1.1 - 1.1 \\ det =1 - 1 \\ det =0$