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Question 1194923: Please help me solve this Linear Equation using Matrices:
Solve the following system of equations by reducing the augmented matrix.
4x1 − 8x2 + 4x3 = 48
4x2 + 8x3 = 16
1.5x1 + x2 − 2.5x3 = −2
(x1, x2, x3) =
Answer by ikleyn(52879)   (Show Source):
You can put this solution on YOUR website! .
Please help me solve this Linear Equation using Matrices:
Solve the following system of equations by reducing the augmented matrix.
4x1 − 8x2 + 4x3 = 48
4x2 + 8x3 = 16
1.5x1 + x2 − 2.5x3 = −2
(x1, x2, x3) =
~~~~~~~~~~~~~~~~~~
S o l u t i o n
Your matrix
X1 X2 X3 b
1 4 -8 4 48
2 0 4 8 16
3 1.5 1 -2.5 -2
Make the pivot in the 1st column by dividing the 1st row by 4
X1 X2 X3 b
1 1 -2 1 12
2 0 4 8 16
3 1.5 1 -2.5 -2
Multiply the 1st row by 1.5
X1 X2 X3 b
1 1.5 -3 1.5 18
2 0 4 8 16
3 1.5 1 -2.5 -2
Subtract the 1st row from the 3rd row and restore it
X1 X2 X3 b
1 1 -2 1 12
2 0 4 8 16
3 0 4 -4 -20
Make the pivot in the 2nd column by dividing the 2nd row by 4
X1 X2 X3 b
1 1 -2 1 12
2 0 1 2 4
3 0 4 -4 -20
Multiply the 2nd row by -2
X1 X2 X3 b
1 1 -2 1 12
2 0 -2 -4 -8
3 0 4 -4 -20
Subtract the 2nd row from the 1st row and restore it
X1 X2 X3 b
1 1 0 5 20
2 0 1 2 4
3 0 4 -4 -20
Multiply the 2nd row by 4
X1 X2 X3 b
1 1 0 5 20
2 0 4 8 16
3 0 4 -4 -20
Subtract the 2nd row from the 3rd row and restore it
X1 X2 X3 b
1 1 0 5 20
2 0 1 2 4
3 0 0 -12 -36
Make the pivot in the 3rd column by dividing the 3rd row by -12
X1 X2 X3 b
1 1 0 5 20
2 0 1 2 4
3 0 0 1 3
Multiply the 3rd row by 5
X1 X2 X3 b
1 1 0 5 20
2 0 1 2 4
3 0 0 5 15
Subtract the 3rd row from the 1st row and restore it
X1 X2 X3 b
1 1 0 0 5
2 0 1 2 4
3 0 0 1 3
Multiply the 3rd row by 2
X1 X2 X3 b
1 1 0 0 5
2 0 1 2 4
3 0 0 2 6
Subtract the 3rd row from the 2nd row and restore it
X1 X2 X3 b
1 1 0 0 5
2 0 1 0 -2
3 0 0 1 3
Solution set:
x1 = 5
x2 = -2
x3 = 3
Solved.
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