Use Gaussian elimination to solve the following system of linear equations -2x_1+3x_2 + x_3 = 2 -3x_1+4x_2 + 2x_3 = 2 x_1-5x_2+4x_3 = -9 -2x_1+4x_2-4x_3 = 8

Answers

Answer 1

Answer:

To solve the system of linear equations using Gaussian elimination, we'll write the augmented matrix and perform row operations to transform it into row echelon form.

The given system of equations:

-2x_1 + 3x_2 + x_3 = 2

-3x_1 + 4x_2 + 2x_3 = 2

x_1 - 5x_2 + 4x_3 = -9

-2x_1 + 4x_2 - 4x_3 = 8

Writing the augmented matrix:

[ -2 3 1 | 2 ]

[ -3 4 2 | 2 ]

[ 1 -5 4 | -9 ]

[ -2 4 -4 | 8 ]

1. Row 1 Ã (-3) + Row 2 â Row 2:

[ -2 3 1 | 2 ]

[ 9 -13 -5 | -6 ]

[ 1 -5 4 | -9 ]

[ -2 4 -4 | 8 ]

2. Row 1 Ã (1/2) + Row 3 â Row 3:

[ -2 3 1 | 2 ]

[ 9 -13 -5 | -6 ]

[ -1 (3/2) 2 | -5/2]

[ -2 4 -4 | 8 ]

3. Row 1 Ã (-1) + Row 4 â Row 4:

[ -2 3 1 | 2 ]

[ 9 -13 -5 | -6 ]

[ -1 (3/2) 2 | -5/2]

[ 0 7 -3 | 6 ]

4. Row 2 Ã (-9/7) + Row 3 â Row 3:

[ -2 3 1 | 2 ]

[ 9 -13 -5 | -6 ]

[ -1 0 (59/7) | -(23/7)]

[ 0 7 -3 | 6 ]

5. Row 2 Ã (2/3) + Row 4 â Row 4:

[ -2 3 1 | 2 ]

[ 9 -13 -5 | -6 ]

[ -1 0 (59/7) | -(23/7)]

[ 0 0 (-11/7) | 0 ]

6. Row 3 Ã (-14/11) + Row 4 â Row 4:

[ -2 3 1 | 2 ]

[ 9 -13 -5 | -6 ]

[ -1 0 (59/7) | -(23/7)]

[ 0 0 1 | 0 ]

7. Row 3 Ã (1/2) + Row 1 â Row 1:

[ -1 3/2 3/2 | (4/7) ]

[ 9 -13 -5 | -6 ]

[ -1 0 1 | 0 ]

[ 0 0 1 | 0 ]

8. Row 3 Ã (9/7) + Row 2 â Row 2:

[ -1 3/2 3/2 | (4/7) ]

[ 0 -26/7 -14/7 | -42/7 ]

[ -1 0 1 | 0 ]

[ 0 0 1 | 0 ]

9. Row 3 Ã (1/2) + Row 4 â Row 4:

[ -1 3/2 3/2 | (4/7) ]

[ 0 -26/7 -14/7 | -42/7 ]

[ -1 0 1 | 0 ]

[ 0 0 1 |

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Answers

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Answers

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............................................

Answer:

^he right

Step-by-step explanation:

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Answers

Answer:

See below.

Step-by-step explanation:

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Do you want them solved?

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Answers

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