Solve the following systems of homogeneous linear equations by matrix method:3x – y + 2z = 04x + 3y + 3z = 05x + 7y + 4z = 0

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

3x – y + 2z = 0
4x + 3y + 3z = 0
5x + 7y + 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

Step 7

Now, |A| = 3(12 – 21) + 1(16 – 15) + 2(28 – 15)= 0. Hence, the system has infinite solutions.

Let z = k
3x – y = – 2k
4x + 3y = – 3k