Question

Solve the systems of homogeneous linear equations by matrix method:

3x – y + 2z = 0
4x + 3y + 3z = 0
5x + 7y + 4z = 0

Answer 1

Given as 3x – y + 2z = 0

4x + 3y + 3z = 0

5x + 7y + 4z = 0

The equation can be written as

AX = 0

Then, |A| = 3(12 – 21) + 1(16 – 15) + 2(28 – 15)

|A| = – 27 + 1 + 26

|A| = 0

So, the system has infinite solutions

Suppose z = k

3x – y = – 2k

4x + 3y = – 3k

So, x = (-9k/13), y = (-k/13) and z = k