Solve the following systems of homogeneous linear equations by matrix method:
3x + y – 2z = 0
x + y + z = 0
x – 2y + z = 0
The system can be written as
A X = 0
Now, |A| = 3(1 + 2) – 1(1 – 1) – 2(– 2 – 1) = 0
|A| = 9 – 0 + 6
|A| = 15
Hence, the given system has only trivial solution given by x = y = z = 0