Question

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

3x – y + 2z = 0

4x + 3y + 3z = 0

5x + 7y + 4z = 0

Answer 1

The system can be written as

A X = 0

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

|A| = – 27 + 1 + 26 |A| = 0

Hence, the system has infinite solutions

Let z = k

3x – y = – 2k

4x + 3y = – 3k

Hence, x = \(\frac{-9k}{13},\) y = \(\frac{-k}{13}\) and z = k