Question

Solve the following systems of homogeneous linear equations by matrix method:

x + y – 6z = 0
x – y + 2z = 0
– 3x + y + 2z = 0

Answer 1

Given as x + y – 6z = 0

x – y + 2z = 0

– 3x + y + 2z = 0

The equation can be written as

A X = 0

Then, |A| = 1(– 2 – 2) – 1(2 + 6) – 6(1 – 3)

|A| = – 4 – 8 + 12

|A| = 0

So, the system has infinite solutions

Suppose z = k

x + y = 6k

x – y = – 2k

So, x = 2k, y = 4k and z = k