Solve the following systems of homogeneous linear equations by matrix method:
2x – y + z = 0
3x + 2y – z = 0
X + 4y + 3z = 0
The system can be written as
A X = 0
Now, |A| = 2(6 + 4) + 1(9 + 1) + 1(12 – 2)
|A| = 2(10) + 10 + 10
|A| = 40 ≠ 0
Since, |A|≠ 0, hence x = y = z = 0 is the only solution of this homogeneous equation.