Question

calcule det A, det B, det (A+B) e det (A.B) me ajudem!

Answer 1

Resposta:

A = $\left[\begin{array}{ccc}a11&a12&a13\\a21&a22&a23\\a31&a32&a33\end{array}\right] \\\\\\\left[\begin{array}{ccc}1&2&2\\1&1&2\\1&1&1\end{array}\right]$

B = $\left[\begin{array}{ccc}-1&1&1\\-1&-1&1\\-1&-1&-1\end{array}\right]$

Det A =

$\left[\begin{array}{ccc}1&2&2\\1&1&2\\1&1&1\end{array}\right] . \left[\begin{array}{ccc}1&2\\1&1\\1&1\end{array}\right]\\\\\\= (1 . 1 . 1) + (2 . 2 . 1) + (2 . 1 . 1) - (2 . 1 . 1) - (1 . 2 . 1) - (2 . 1 . 1)\\\\= 1 + 4 + 2 - 2 - 2 - 2\\\\= 1$

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Det B =

$\left[\begin{array}{ccc}-1&1&1\\-1&-1&1\\-1&-1&-1\end{array}\right] . \left[\begin{array}{ccc}-1&1\\-1&-1\\-1&-1\end{array}\right]\\\\\\= (-1 . -1 . -1) + (1 . 1 . -1) + (1 . -1 . -1) - (1 . -1 . -1) - (-1 . 1 . -1) - (1 . -1 . -1)\\\\= -1 -1 +1 -1 -1 -1\\\\= -4$

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A+B =

$\left[\begin{array}{ccc}1&2&2\\1&1&2\\1&1&1\end{array}\right] + \left[\begin{array}{ccc}-1&1&1\\-1&-1&1\\-1&-1&-1\end{array}\right]\\\\\\= \left[\begin{array}{ccc}0&3&3\\0&0&3\\0&0&0\end{array}\right]$

Det (A+B)=

$\left[\begin{array}{ccc}0&3&3\\0&0&3\\0&0&0\end{array}\right] . \left[\begin{array}{ccc}0&3\\0&0\\0&0\end{array}\right]\\\\\\= (0 . 0 . 0) + (3 . 3 . 0) + (3 . 0 . 0) - (3 . 0 . 0) - (0 . 3 . 0) - (3 . 0. 0)\\\\= 0 + 0 + 0 - 0 - 0 - 0\\\\= 0$

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A . B =

$\left[\begin{array}{ccc}1&2&2\\1&1&2\\1&1&1\end{array}\right] . \left[\begin{array}{ccc}-1&1&1\\-1&-1&1\\-1&-1&-1\end{array}\right]\\\\\\= \left[\begin{array}{ccc}(1.-1 + 2.-1 + 2.-1)&(1.1 + 2.-1 + 2.-1)&(1.1 + 2.1 + 2.-1)\\(1.-1 + 1.-1 + 2.-1)&(1.1 + 1.-1 + 1.-1)&(1.1 + 1.1 + 2.-1)\\(1.-1 + 1.-1 + 1.-1)&(1.1 + 1.-1 + 1.-1)&(1.1 + 1.1 + 1.-1)\end{array}\right]\\\\\\= \left[\begin{array}{ccc}-5&-3&1\\-4&-1&0\\-3&-1&1\end{array}\right]$

Det ( A . B) =

$\left[\begin{array}{ccc}-5&-3&1\\-4&-1&0\\-3&-1&1\end{array}\right] . \left[\begin{array}{ccc}-5&-3\\-4&-1\\-3&-1\end{array}\right]\\\\\\= (-5 . -1 . 1) + (-3 . 0 . -3) + (1 . -4 . -1) - (1 . -1 . -3) - (-5 . 0 . -1) - (-3 . -4 . 1)\\\\= 5 + 0 + 4 -3 - 0 - 12\\\\= -6$

Answer 2

Resposta:

Olá bom dia!

Segue o anexo.

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