Echelon Miner · MAT 331

Problem

Highlight leading entries

Row operation

Type of row operation Replacement Interchange Scaling

No steps yet.

Echelon form

Any rows of all zeros are at the bottom.
Each leading entry (first nonzero entry of a row) is in a column to the right of the leading entry in the row above.
Every entry below a leading entry is 0.

Reduced echelon form

Echelon form, and also:

Pivots and solutions

A pivot position is where a leading entry sits in an echelon form of the matrix (a leading 1 in its reduced echelon form). A pivot column contains a pivot position, and a pivot is the nonzero number there.
Two matrices are row equivalent if row operations turn one into the other.
For an augmented matrix, variables in pivot columns are basic; the others are free.
A system is consistent exactly when the last column is not a pivot column. A consistent system has a unique solution exactly when there are no free variables.

Row operations

Finding

Row reduce [A | I]. If A is row equivalent to I, then [A | I] is row equivalent to [I | A inverse]. Otherwise A is not invertible.