To fill: the blank in the given statement..
Answer to Problem 2E
A matrix in row echelon form is in reduced row echelon form when every column that has a leading 1 has zeros in every position above and below its leading 1.
Explanation of Solution
Given information:
Given statement is
A matrix in row echelon form is in --------when every column that has a leading 1 has zeros in every position above and below its leading 1.
A matrix is in row echelon form if it has the following properties:
- Any rows consisting entirely of zeros at the bottom of the matrix.
- For each row that does not consist entirely of zeros, the first nonzero entry is 1.
- For two successive rows, the leading 1 in the higher row is further to the left than the leading 1 in the lower row.
A matrix in row echelon form is in reduced row echelon form when every column that has a leading 1 has zeros in every position above and below its leading 1.
Consider the augmented matrix is given by
Now, perform row operations as shown:
Apply
Apply
Apply
The above is the reduced row-echelon form of the given matrix.
Chapter 7 Solutions
Precalculus with Limits: A Graphing Approach
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