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

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

x + y – 6z = 0
x – y + 2z = 0
– 3x + y + 2z = 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

Step 7

Now, |A| = 1(– 2 – 2) – 1(2 + 6) – 6(1 – 3)= 0
Hence, the system has infinite solutions

Let z = k
X + y = 6k
x – y = – 2k