Question

The reduced row-echelon form of the augmented matirx of a system of equations is given. Find the solution of the system.

Answer 1

option C)

(19,2,5)

Explanation:

| 4 | x

| 12 | y

| 5 | z

After reducing the matrix in row-echelon form we are left with three equation as following

Equation 1

0x + 0y + 1z = 5

Equation 2

0x + y1 + 2z = 12

Equation 3

1x + 0y -3z = 4

Solution

As in first equation

0 + 0 + z = 5

z = 5

Put this value of z in equation 2 and 3

y + 2(5) = 12

y + 10 =12

y = 12 - 10

y = 2

x + 0 -3(5) = 4

x - 15 = 4

x = 4 + 15

x = 19

So the solution of the system is (x,y,z) = (19,2,5)