Question

Given that the matrix [[-3,-7,-2,0],[3,0,-6,0],[1,7,-2,0]] is the augmented matrix for a linear system, use technology to...

Given that the matrix

[[-3,-7,-2,0],[3,0,-6,0],[1,7,-2,0]]

is the augmented matrix for a linear system, use technology to perform the row operations needed to transform the matrix to reduced echelon form. Then determine if the system is consistent and if it is, find all solutions to the system.

Reduced echelon form:

Is the system consistent?  select yes no

Solution: (x1,x2,x3)=

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Answer #1

for this rows, augmented matrix is

-3 -7 -2 0
3 0 -6 0
1 7 -2 0

convert into Reduced Row Eschelon Form...

Divide row1 by -3

1 7/3 2/3 0
3 0 -6 0
1 7 -2 0


Add (-3 * row1) to row2

1 7/3 2/3 0
0 -7 -8 0
1 7 -2 0


Add (-1 * row1) to row3

1 7/3 2/3 0
0 -7 -8 0
0 14/3 -8/3 0


Divide row2 by -7

1 7/3 2/3 0
0 1 8/7 0
0 14/3 -8/3 0


Add (-14/3 * row2) to row3

1 7/3 2/3 0
0 1 8/7 0
0 0 -8 0


Divide row3 by -8

1 7/3 2/3 0
0 1 8/7 0
0 0 1 0


Add (-8/7 * row3) to row2

1 7/3 2/3 0
0 1 0 0
0 0 1 0


Add (-2/3 * row3) to row1

1 7/3 0 0
0 1 0 0
0 0 1 0


Add (-7/3 * row2) to row1

1 0 0 0
0 1 0 0
0 0 1 0

here for every column there is one pivot entry so system is consistent

so unique solution is

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