8.5. Row Operations and Row Echelon Forms http://www.ck12.org
A I G
B H F
C D E
Every matrix may have a different strategy and as long as you use the three row operations, you will be on the right
track. One thing to be very careful of is to try to avoid fractions within your matrix. Scale the row to eliminate the
fraction.
Concept Problem Revisited
There are two forms of a matrix that are most simplified. The most important is reduced row echelon form that
follows the four stipulations from the guidance section. An example of a matrix in reduced row echelon form is:
1 0 0 2 43
0 1 0 2 3
0 0 1 98 5
Vocabulary
Row operationsare swapping rows, adding a multiple of one row to another or scaling a row by multiplying through
by a scalar.
Row echelon formis a matrix that has a leading one at the start of every non-zero row, zeros below every leading
one and all rows containing only zeros at the bottom of the matrix.
Reduced row echelon formis the same as row echelon form with one additional stipulation: that every other entry
in a column with a leading one must be zero.
Guided Practice
- Reduce the following matrix to reduced row echelon form.
[0 4 5
2 6 8]
- Reduce the following matrix to row echelon form.
3 6
2 4
5 17
- Reduce the following matrix to reduced row echelon form.
[ 3 4 1 0
5 −1 0 1]
Answers:
1.[
0 4 5
2 6 8