Question

Solve the systems of homogeneous linear equations by matrix method: 

2x – y + z = 0

3x + 2y – z = 0

x + 4y + 3z = 0

Answer 1

Given as

2x – y + z = 0

3x + 2y – z = 0

X + 4y + 3z = 0

The equation can be written as

AX = 0

|A| = 2(6 + 4) + 1(9 + 1) + 1(12 – 2)

|A| = 2(10) + 10 + 10

|A| = 40 ≠ 0

So, |A| ≠ 0, thus x = y = z = 0 is the only solution of this homogeneous equation.