Write the matrix in row-echelon form. (Note: Row-echelon forms are not unique.)

Question

1 2 -1 6

3 7 -5 5

-2 -1 -3 2

= ____ _____ ____ ____

____ _____ ____ ____

____ _____ ____ ____

Answer 1

1 2 -1 6

3 7 -5 5

-2 -1 -3 2

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row2 = -3 * row1 + row2;

row3 = 2 * row1 + row3;

1 2 -1 6

0 1 -2 -13

0 3 -5 14

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row1 = -2 * row2 + row1;

row3 = -3 * row2 + row3;

1 0 3 32

0 1 -2 -13

0 0 1 53

z = 53

y - 2(53) = -13

y - 106 = -13

y = 93

x + 3(53) = 32

x + 159 = 32

x = -127

x=-127, y = 93, z=53

Answer 2

1 0 0 -127

0 1 0 93

0 0 1 53