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

There are three types of matrix row operations. First, swapping any two rows in a matrix. Second, multiplying a row by a non-zero scalar. Lastly, adding or subtracting a multiple of one row to another row.

Step 1: Description and Example of Operation One

The first matrix row operation is swapping any two rows in a matrix. If we have matrix A as : \[ \begin{bmatrix} a & b \ c & d \end{bmatrix} \], we can swap the two rows to have: \[ \begin{bmatrix} c & d \ a & b \end{bmatrix} \]

Step 2: Description and Example of Operation Two

The second type of matrix row operation is multiplying a row by a non-zero scalar. In case we have a matrix A as : \[ \begin{bmatrix} a & b \ c & d \end{bmatrix} \], we can multiply the second row by 2 to get: \[ \begin{bmatrix} a & b \ 2c & 2d \end{bmatrix} \]

Step 3: Description and Example of Operation Three

The third type of matrix row operation is adding or subtracting a multiple of one row to another row. For instance, if we have a matrix A as : \[ \begin{bmatrix} a & b \ c & d \end{bmatrix} \], we can subtract the first row from the second to get: \[ \begin{bmatrix} a & b \ c-a & d-b \end{bmatrix} \]