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

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

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

Step 1

Step 2

Step 3

Step 4

Step 5

Now, |A| = 2(6 + 4) + 1(9 + 1) + 1(12 – 2)

|A| = 2(10) + 10 + 10

|A| = 40 ≠ 0

Since, |A|≠ 0, hence x = y = z = 0 is the only solution of this homogeneous equation.