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


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