Solve the following systems of homogeneous linear equations by matrix method:x + y – z = 0x – 2y + z = 03x + 6y

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

x + y – z = 0
x – 2y + z = 0
3x + 6y – 5z = 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(4) – 1(– 8) – 1(12) = 0
Hence, the system has infinite solutions
Let z = k, X + y = k, x – 2y = – k