Indicate which of the following are in row echelon form and

Indicate which of the following are in row echelon form and which are in reduced row echelon form: (a) [1 0 2 1 0 0 1 1] Row echelon form?: yes no Reduced row echelon form?: yes no (b) [1 0 0 0 0 0 0 0 1] Row echelon form?: yes no Reduced row echelon form?: yes no (c) [1 3 1 0 0 1 0 0 0] Row echelon form?: yes no Reduced row echelon form?: yes no (d) [1 1 0 0 0 0 0 0] Row echelon form?: yes no Reduced row echelon form?: yes no (e) [1 0 0 0 3 0 1 0 0 1 0 0 1 0 -6 0 0 0 1 1] Row echelon form?: yes no Reduced row echelon form?: yes no

Solution

A matrix that has undergone Gaussian elimination is said to be in row echelon form or, more properly, \"reduced echelon form\" or \"row-reduced echelon form if the new matrix has the following characteristics:

1. All zero rows are at the bottom of the matrix

2. The leading entry of each nonzero row after the first occurs to the right of the leading entry of the previous row.

3. The leading entry in any nonzero row is 1.

4. All entries in the column above and below a leading 1 are zero.

(a) No

(b) Yes

(c) No

(d) Yes

(e) Yes