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Row echelon form of matrix

Find the row echelon form (not the reduced row echelon form) of the 4 X 3 matrix whose rows are as follows:

row 1: 1/3 1/4 1/5

row 2: 2/3 2/4 2/5

row 3: 3/3 3/4 3/5

row 4: 4/3 4/4 4/5

Solution Preview

In the first step, do the following:

a. Retain the existing row 1.

b. To get the new row 2, multiply row 1 by -2, and add the result to the existing row 2. Thus the new row 2 is 0, 0, 0, since

(i) (-2)*(1/3) = -2/3, and (-2/3) + 2/3 = 0
(ii) (-2)*(1/4) = -2/4, and (-2/4) + 2/4 = 0
(iii) (-2)*(1/5) = -2/5, and (-2/5) + 2/5 = 0

c. To get the new row 3, multiply row 1 by -3, and add the result to the existing row 3. Thus the new row 3 is 0, 0, 0, since

(i) (-3)*(1/3) = -3/3, and (-3/3) + 3/3 = 0
(ii) ...

Solution Summary

A detailed, step-by-step determination of the row echelon form of the given matrix is provided.

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