Question

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

2x – y + 2z = 0

5x + 3y – z = 0

X + 5y – 5z = 0

Answer 1

The system can be written as

A X = 0

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

|A| = – 20 – 24 + 44

|A| = 0

Hence, the system has infinite solutions

Let z = k

2x – y = – 2k

5x + 3y = k

Hence, x = \(\frac{-5k}{11},\) y = \(\frac{12k}{11}\) and z = k