Solve the following systems of homogeneous linear equations by matrix method:2x – y + 2z = 0, 5x + 3y – z = 0,X + 5y

Solve the following systems of homogeneous linear equations by matrix method:2x – y + 2z = 0, 5x + 3y – z = 0,X + 5y – 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

Step 7

Step 8

A X = 0
Now, |A| = 2(– 15 + 5) + 1(– 25 + 1) + 2(25 – 3)= 0

Hence, the system has infinite solutions

Let z = k
2x – y = – 2k
5x + 3y = k