Augmented matrix to row echelon or triangular form?

Question

I have a question on my math HW and i cant figure it out.

For the system of equations given, write the augmented matrix. Use matrix row operations to put the matrix into row echelon or triangular form. Then solve the system.

x+2y+7z=5
5x -3z=8
2x-y =0



Any help would be awesome

Answer 1

[1 2 7 5]
[5 0 -3 8]
[2 -1 0 0]

swap row 2 and row 3:
[1 2 7 5]
[2 -1 0 0]
[5 0 -3 8]

add 2 times row 2 to row 1:
[5 0 7 5]
[2 -1 0 0]
[5 0 -3 8]

subtract row 1 from row 3:
[5 0 7 5]
[2 -1 0 0]
[0 0 -10 3]

subtract 2 times row 1 from 5 times row 3:
[5 0 7 5]
[0 -5 -14 0 -10]
[0 0 -10 3]

multiply row 1 by 10, row 2 by -1, row 3 by -1:
[50 0 70 50]
[0 5 14 0 10]
[0 0 10 -3]

subtract 7 times row 3 from row 1:
[50 0 0 71]
[0 5 14 0 10]
[0 0 10 -3]

multiply row 2 by 5 and row 3 by 7:
[50 0 0 71]
[0 25 70 0 50]
[0 0 70 -21]

subtract row 3 from row 2:
[50 0 0 71]
[0 25 0 71]
[0 0 70 -21]

divide row 1 by 50, row 2 by 25, row 3 by 70:
[1 0 0 71/50]
[0 1 0 71/25]
[0 0 0 -3/10]

this is not quite as direct as what you're taught, but it avoids fractions until the last step.