Question

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

x + y + z = 0

x – y – 5z = 0

x + 2y + 4z = 0

Answer 1

The system can be written as

A X = 0

Now, |A| = 1(6) – 1(9) + 1(3) = 0

|A| = 6 – 9 + 3

|A| = 0

Hence, the system has infinite solutions

Let z = k

X + y = – k

x – y = 5k

Hence, x = 2k, y = – 3k and z = k