Reduced row echelon form: Difference between revisions

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Your algorithm/function does NOT work

The "SWAP" is not being done.

Try this matrix to see the problem.

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Linear Algebra with Applications by W. Keith Nicholson, University of Calgary

page 12 - Systems of Linear Equations

Solve the following system of equations.

3x + y − 4z = −1

x + 10z = 5

4x + y + 6z = 1

Solution. The corresponding augmented matrix is

3 1 −4 −1

1 0 10 5

4 1 6 1

Create the first leading one by interchanging rows 1 and 2

1 0 01 5

3 1 −4 −1

4 1 6 1

Now subtract 3 times row 1 from row 2, and subtract 4 times row 1 from row 3. The result is

1 0 10 5

0 1 −34 −16

0 1 −34 −19

Now subtract row 2 from row 3 to obtain

1 0 10 5

0 1 −34 −16

0 0 0 −3

This means that the following reduced system of equations

x + 10z = 5

y − 34z = −16

0 +0 +0 = −3

is equivalent to the original system. In other words, the two have the same solutions.

But this last system clearly has no solution (the last equation requires that x, y and z satisfy 0x+0y+0z = −3,

and no such numbers exist).

Hence the original system has no solution.

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