Question

Using matrix, solve the following system o equations. 

4x + 3y + 2z = 60, x + 2y + 3z = 45, 6x + 2y + 3z = 70

Answer 1

4x + 3y + 2z = 60

x + 2y + 3z = 45

6x + 2y + 3z = 70

Convert the equations into matrix form AX = B

4R₂ - R₁ → R₂

2R₃ - 3R₁ → R₃

Again convert the matrix form into equations,

4x + 3y + 2z = 60    .......(1)

5y + 10z = 120   .......(2)

-5y = -40      .......(3)

Thus,

\(y = \frac {40}5 = 8\)

Substitute y = 8 in eq.(2)

5 x 8 + 10z = 120

40 + 10z = 120

10z = 80 

⇒ z =  8

Substitute y = 8, z = 8 in eq.(1)

4x + 24 + 16 = 60

4x = 20 

⇒ x = 5

Therefore, x = 5, y =  8, and z = 8.

Answer 2

Given system o equations can be written as