Question

2) CALCULE AS DETERMINANTES, REGRA DE SARRUS:
a)
B= l 1,5,-2 l
l 8,3,0 l
l 4,-1,2 l

b
A= ( 1,2,1 )
( 4,9,7 )
( 6 x x -7)​

Answer 1

Vamos calcular o determinante das matrizes pela Regra de Sarrus que foi solicitado. Para isso, repita as duas colunas inicias ao lado da matriz, multiplique a diagonal principal, e subtraia da multiplicação da diagonal secundária

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$\begin{array}{l}\underbrace{\sf Veja:}\end{array}$

Letra A)

$\begin{array}{l}\sf B=\begin{bmatrix}\sf1&\sf5&\sf-2\\\sf8&\sf3&\sf0\\\sf4&\sf-1&\sf2\end{bmatrix}\\ \\ \sf Det(B)=\begin{vmatrix}\sf1&\sf5&\sf-2 \\ \sf8&\sf3&\sf0 \\ \sf4&\sf-1&\sf2\end{vmatrix}\begin{matrix}\sf1&\sf5\\ \sf8&\sf3 \\\sf4&\sf-1 \end{matrix}\\ \\ \sf Det(B)=1.3.2+5.0.4+(-2).8.(-1)-[(-2).3.4+1.0.(-1)+5.8.2] \\ \\ \sf Det(B)=6+0+16-[-24-0+80] \\ \\ \sf Det(B)=22-[56] \\ \\ \sf Det(B)=22-56 \\ \\ \!\boxed{\sf Det(B)=-34}\end{array}$

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Letra B)

$\begin{array}{l}\sf A=\begin{pmatrix}\sf1&\sf2&\sf1 \\ \sf4&\sf9&\sf7 \\ \sf6&\sf x&\sf x-7\end{pmatrix} \\ \\ \sf Det(A)=\begin{vmatrix}\sf1&\sf2&\sf1 \\ \sf4&\sf9&\sf7 \\ \sf6&\sf x&\sf x-7\end{vmatrix}\begin{matrix}\sf1&\sf2 \\ \sf4&\sf9 \\ \sf6&\sf x\end{matrix} \\ \\ \sf Det(A)=1.9.(x-7)+2.7.6+1.4.x-[1.9.6+1.7.x+2.4.(x-7)] \\ \\ \sf Det(A)=9x-63+84+4x-[54+7x+8x-56] \\ \\ \sf Det(A)=13x+21-[-2+15x] \\ \\ \sf Det(A)=13x+21+2-15x\\ \\\!\boxed{\sf Det(A)=-2x+23}\end{array}$

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Att. Nasgovaskov

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