We summarize the notation to keep track of the precise row operations being used.
Type I operation
What it does: switches and rows.
Type II operation
What it does: multiplies row by .
Type III operation
What it does: adds times the row to the row
Indicated by: or “ added to ”
Suppose we started with the same matrix, but performed a type II operation instead,
where the second row is multiplied by . Then using the above conventions, we would
denote that by
Suppose we started with the same matrix, but performed a type III operation, where
the second row is multiplied by and added to the first row. Then using the above
conventions, we would denote that by
In the following exercises, fill in the blank with the indicated row operation needed to produce the matrix on the right from the matrix on the left.