Elementary Row Operations (Linear Algebra)

0:00 What Are Elementary Row Operations?
0:23 Interchange (Swapping Rows)
0:59 Scaling (Multiply a Row By a Constant)
1:48 Replacement (Adding Rows to Other Rows)
3:09 Review & List of Row Operations

This video explain the three elementary row operations for matrices in linear algebra. Elementary row operations are useful for elimination within a matrix and getting a matrix into echelon form or reduced echelon form.

Interchange is the idea that we can swap any two rows of a matrix just as we can change the order of equations in a system of linear equations, and it does not affect the solution.

Scaling means that we multiply a row by a nonzero constant to obtain a multiple of that row in the matrix. This can be used to get a leading entry of 1 in a row, and it may also be used as part of the elimination process used in replacement.

Replacement allows us to add a multiple of a row to another row. This is particularly useful when obtaining zeros in certain entries of the matrix to put it into echelon form or reduced echelon form.