Question

QUESTION 3 Given the following equations: 2x + 3y + z = 13 3x – 4y + 2z=3 x + y + z = 6 Determine x, y, and z. X = , y = and z =

Answer 1

we are given system of equations as

2.c + 3y +z= 13

3.r – 4y + 2z = 3

T+y+z=6

Firstly, we will find augmented matrix

A= 2 3 1 3 1 -4 2 1 1 13 3 6

now, we can change into reduced row-echelon form

step-1: multiply the 1st row by 1/2

A= ſi 3/2 1/2 13/2 3 -4 2 3 1 1 1 6

step-2: add -3 times the 1st row to the 2nd row

A= ſi 0 1 3/2 -17/2 1 1/2 1/2 1 13/2 -33/2 6

step-3: add -1 times the 1st row to the 3rd row

|1 32 12 132 A = 10 -172 12 -33/2 |0 -12 12 -1/2

step-4:multiply the 2nd row by -2/17

A = 1 0 0 3/2 1 -1/2 1/2 -1/17 1/2 13/2 33/17 -1/2

step-5: add 1/2 times the 2nd row to the 3rd row

A= (1 3/2 0 1 0 0 1/2 13/2 -1/17 33/17 8/17 8/17

step-6: multiply the 3rd row by 17/8

A= (1 3/2 0 1 0 0 1/2 13/2 -1/17 33/17 1 1

step-7: add 1/17 times the 3rd row to the 2nd row

A= 1 3/2 1/2 13/2 0 1 0 2 0 0 1 1

step-8: add -1/2 times the 3rd row to the 1st row

A= 1 0 0 3/2 1 0 0 6 0 2 1 1

step-9: add -3/2 times the 2nd row to the 1st row

1 0 0 3 A= 01 02 0 0 1 1

so, we get solution as

..............Answer

x = 3, y = 2,2=1