Question

metodo de los determinantes
4x+y+ 2z=27
x+2y+z=13
2x+3y+z=21 ​

Answer 1

Explicación paso a paso:

$D = \left | \begin{array}{ccccc} 4 & 1& 2\\ 1&2&1\\ 2&3&1 \\ 4& 1&2 \\ 1&2&1\end{array}\right | = + (8 + 6 + 2) - (8 + 12 + 1) \\ = 16 - 21 \\ D= - 5 \\ \\D_x = \left | \begin{array}{ccccc} 27 & 1& 2\\ 13&2&1\\ 21&3&1 \\ 27& 1&2 \\ 13&2&1\end{array}\right | = + (54 + 78 + 21) - (84 + 81 + 13) \\ = 153 - 178\\ D_x = - 25\\ \\ D_y = \left | \begin{array}{ccccc} 4 & 27& 2\\ 1&13&1\\ 2&21&1 \\ 4& 27&2 \\ 1&13&1\end{array}\right | = +(52 + 42 + 54) - (52 + 84 + 27) \\ = 148- 163 \\ D_y = - 15 \\ \\ D_z =\left | \begin{array}{ccccc} 4& 1&27\\ 1&2&13\\ 2&3&21 \\ 4& 1&27\\ 1&2&13\end{array}\right | = + (168 + 81 + 26) - (108 + 156 + 21) \\ = 275 - 285 \\ D_z = - 10$

x = D(x)/D

x = -25/-5

x = 5

y = D(y)/D

y = -15/-5

y = 3

z = D(z)/D

z = -10/-5

z = 2