Question

Solve the system of homogeneous equations:
3x + y - 2z = 0
x + y + z = 0
x - y + z = 0

Answer 1

Answer:

$x=0,y=0,z=0$

Step-by-step explanation:

Cramer's Rule:

it says that

$x=\frac{\triangle}{\triangle_{1}}\\\\\\y=\frac{\triangle}{\triangle_{2}}\\\\\\z=\frac{\triangle}{\triangle_{3}}$

where Δ is determinant of matrix A,Δ1,Δ2,Δ3 are the determinant of A when column 1,2,3 are replaced by coefficient matrix respectively.$\triangle=\left|\begin{array}{ccc}3&1&-2\\1&1&1\\1&-1&1\end{array}\right|=8$

$\triangle_{1}=\left|\begin{array}{ccc}0&1&-2\\0&1&1\\0&-1&1\end{array}\right|=0$

$\triangle_{2}=\left|\begin{array}{ccc}3&0&-2\\1&0&1\\1&0&1\end{array}\right|=0$

$\triangle_{3}=\left|\begin{array}{ccc}3&1&0\\1&1&0\\1&-1&0\end{array}\right|=0$

$x=\frac{0}{8} ,y=\frac{0}{8},z=\frac{0}{8}\\\\x=0,y=0,z=0$