Question

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

x + y – z = 0

x – 2y + z = 0

3x + 6y – 5z = 0

Answer 1

The system can be written as

A X = 0

Now, |A| = 1(4) – 1(– 8) – 1(12) = 0

|A| = 4 + 8 – 12

|A| = 0

Hence, the system has infinite solutions

Let z = k

X + y = k

x – 2y = – k

Hence, x = \(\frac k3,\) y = \(\frac{2k}3\) and z = k