388 CHAPTER 18. LINEAR FUNCTIONS

Now take −3 times the top row and add to the second followed by −1 times the top rowadded to the bottom.  1 −1 3 2

0 5 −8 −50 5 0 0

Now take −1 times the second row and add to the bottom. 1 −1 3 2

0 5 −8 −50 0 8 5

Add the bottom to the second  1 −1 3 2

0 5 0 00 0 8 5

Then take −1/5 times the bottom and add to the top. 1 −1 7

5 10 5 0 00 0 8 5

then take −1/5 times the middle and add to top. Finally divide each row by the numbersdown the diagonal and then take 2 times the middle and add to top then −7/5 times thebottom and add to top.  1 0 0 1

80 1 0 00 0 1 5

8

Finally you get the row reduced echelon form for this matrix.

18.2.1 Using MATLABIt may seem tedious to find the row reduced echelon form. You can let MATLAB do it foryou. Here is an example.

>> A=[1 2 3 4;2 3 -11 12;3 5 6 7];rref(A)ans =1.0000 0 0 -7.92860 1.0000 0 6.92860 0 1.0000 -0.6429

At the >> I entered the matrix

 1 2 3 42 3 −11 123 5 6 7

 . The semicolon indicates you

start a new row. Then press shift enter to get to the next line and press enter and it producesthe row reduced echelon form . It does it in terms of decimals. 1.0 0 0 −7.9286

0 1.0 0 6.92860 0 1.0 −0.64286

