Question

Use Cramer’s rule to solve
x+2y+z=5
2x+2y+z=6
x+2y+3z=9

Answer 1

$D=\begin{vmatrix} 1 & 2 & 1\\ 2 & 2 & 1\\ 1 & 2 &3 \end{vmatrix}=6+2+4-2-2-12=-4$

$D_x=\begin{vmatrix} 5 & 2&1 \\ 6& 2&1\\ 9&2&3 \end{vmatrix}=30+18+12-18-36-10=-4$

$D_y=\begin{vmatrix} 1&5&1\\2&6&1\\1&9&3 \end{vmatrix}=18+18+5-6-30-9=-4$

$D_z=\begin{vmatrix} 1&2&5\\2&2&6\\1&2&9 \end{vmatrix}=18+20+12-10-36-12=-8$

$x=D_x/D=(-4)/(-4)=1;$

$y=D_y/D=(-4)/(-4)=1;$

$z=D_z/D=(-8)/(-4)=2.$

Answer:

$x=1; y=1; z=2.$