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

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

x + y + z = 0
x – y – 5z = 0
x + 2y + 4z = 0

Match the items on the right to the items on the left.

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Now, |A| = 1(6) – 1(9) + 1(3) = 0
Hence, the system has infinite solutions
Let z = k, X + y = – k. x – y = 5k