Resposta:
Explicação passo-a-passo:
a)
Passo 1: calcular o determinante principal, D.
[tex]\left[\begin{array}{ccc}2&-3&4\\3&1&1\\1&2&-2\\2&-3&4\\3&1&1\end{array}\right][/tex]
D = - 4 + 24 - 3 - 4 - 4 - 18 = - 9
Passo 2: calcular o determinante com as respostas na coluna da variável x, Dx.
[tex]\left[\begin{array}{ccc}5&-3&4\\19&1&1\\9&2&-2\\5&-3&4\\19&1&1\end{array}\right][/tex]
Dx = - 10 + 152 - 27 - 36 - 10 - 114 = - 45
[tex]x = \frac{Dx}{D} =\\\\x = \frac{-45}{-9} = 5[/tex]
Passo 3: calcular o determinante com as respostas na coluna da variável y, Dy,
[tex]\left[\begin{array}{ccc}2&5&4\\3&19&1\\1&9&-2\\2&5&4\\3&19&1\end{array}\right][/tex]
D y = - 76 + 108 + 5 - 76 - 18 + 30 = - 27
[tex]y = \frac{Dy}{D} \\\\y = \frac{- 27}{- 9} = 3[/tex]
Passo 4: calcular o determinante com as respostas na coluna da variável z, Dz,
[tex]\left[\begin{array}{ccc}2&-3&5\\3&1&19\\1&2&-9\\2&-3&5\\3&1&19\end{array}\right][/tex]
Dz = - 18 + 30 - 57 - 5 - 76 - 81 = - 207
[tex]z = \frac{Dz}{D} \\\\z = \frac{- 207}{- 9} = 23[/tex]
b)
[tex]D = \left[\begin{array}{ccc}- 3&-4&3\\2&2&2\\2&1&-1\\- 3&-4&3\\2&2&2\end{array}\right][/tex]
D = 6 + 6 - 16 - 12 + 6 - 8 = - 18
[tex]Dx = \left[\begin{array}{ccc}- 15&-4&3\\24&2&2\\9&1&-1\\- 15&-4&3\\24&2&2\end{array}\right] \\[/tex]
D x = 30 + 72 - 72 - 54 + 30 - 96 = -90
x = - 90/-18 = 5
[tex]Dy = \left[\begin{array}{ccc}- 3&-15&3\\2&24&2\\2&9&-1\\- 3&-15&3\\2&24&2\end{array}\right] \\[/tex]
Dy = - 72 + 54 - 60 - 144 + 54 - 30 = - 198
y = - 198/-18 = 11
[tex]Dz = \left[\begin{array}{ccc}- 3&-4&-15\\2&2&24\\2&1&9\\- 3&-4&-15\\2&2&24\end{array}\right] \\[/tex]
Dz = - 54 - 30 - 192 + 60 + 72 + 72 = - 72
z = - 72/-18 = 4
