Solve the following systems of homogeneous linear equations by matrix method:
x + y + z = 0
x – y – 5z = 0
x + 2y + 4z = 0
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
A X = B
|A| = – 1 – 1 = – 2 ≠0 So, A – 1 exist
Now adj A = =
X = A – 1 B =
X =
X =
Hence, x = 2k, y = – 3k and z = k