Solve the following systems of homogeneous linear equations by matrix method: x + y – 6z = 0 x – y + 2z = 0 – 3x + y + 2z = 0

Question

Philoid · Accepted Answer

The system can be written as

A X = 0

Now, |A| = 1(– 2 – 2) – 1(2 + 6) – 6(1 – 3)

|A| = – 4 – 8 + 12

|A| = 0

Hence, the system has infinite solutions

Let z = k

X + y = 6k

x – y = – 2k

A X = B

|A| = – 1 – 1 = – 2 ≠0 So, A ^{– 1} exist

Now adj A = =

X = A ^{– 1} B =

X =

Hence, x = 2k, y = 4k and z = k