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In: Physics

Write the augmented matrix for the following system of linear equations. Solve the equation (x,y,z) by...

Write the augmented matrix for the following system of linear equations. Solve the equation (x,y,z) by row reduction.

x+3y-2z=5

3x+5y+6z=7

2x+4y+3z=8

Expert Solution

Rewrite the system in matrix form and solve it by Gaussian Elimination (Gauss-Jordan elimination)

1	3	-2	5
3	5	6	7
2	4	3	8

from 2; 3 rows we subtract the 1-th row, multiplied respectively by 3; 2

1	3	-2	5
0	-4	12	-8
0	-2	7	-2

devide the 2-th row by -4

1	3	-2	5
0	1	-3	2
0	-2	7	-2

from 1; 3 rows we subtract the 2-th row, multiplied respectively by 3; -2

1	0	7	-1
0	1	-3	2
0	0	1	2

from 1; 2 rows we subtract the 3-th row, multiplied respectively by 7; -3

1	0	0	-15
0	1	0	8
0	0	1	2

	x₁ = -15
	x₂ = 8
	x₃ = 2

genius_generous answered 9 months ago

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