Question

Solve the systems of homogeneous linear equations by matrix method:

2x – y + 2z = 0
5x + 3y – z = 0
X + 5y – 5z = 0

Answer 1

Given as 2x – y + 2z = 0

5x + 3y – z = 0

X + 5y – 5z = 0

The equation can be written as

AX = 0

Then |A| = 2(– 15 + 5) + 1(– 25 + 1) + 2(25 – 3)

|A| = – 20 – 24 + 44

|A| = 0

So, the system has infinite solutions

Suppose z = k

2x – y = – 2k

5x + 3y = k

So, x = -5k/11, y = 12k/11 and z = k