Problem 53 - College Algebra

Question

In your own words, describe each of the three matrix row operations. Give an example with each of the operations.

Step-by-Step Solution

Answer

The three matrix row operations involve 1) swapping two rows, 2) multiplying a row by a non-zero constant, and 3) adding a multiple of one row to another row.

Step 1: Row operation 1: Swapping two rows

This operation involves interchanging two rows. For example, if we have a matrix\[\begin{{pmatrix}}1 & 2 & 3\4 & 5 & 6\\end{{pmatrix}}\]we can swap row 1 and row 2 to get\[\begin{{pmatrix}}4 & 5 & 6\1 & 2 & 3\\end{{pmatrix}}\]

Step 2: Row operation 2: Multiplying a row by a non-zero constant

This operation involves multiplying every element in a row by a non-zero constant. For example, if we multiply the first row of our initial matrix by 2, we get \[\begin{{pmatrix}}2 & 4 & 6\4 & 5 & 6\\end{{pmatrix}}\]

Step 3: Row operation 3: Adding a multiple of one row to another row

This operation involves multiplying a row by a constant and adding it to another row. For instance, if we multiply row 1 by 2 and add it to row 2 in our original matrix, we get \[\begin{{pmatrix}}1 & 2 & 3\6 & 9 & 12\\end{{pmatrix}}\]