Row operations

Definition

Row operations are manipulations of the rows of a matrix to achieve a desired form, typically for solving systems of linear equations. These operations include row swapping, scaling rows, and adding or subtracting multiples of rows.

5 Must Know Facts For Your Next Test

1. There are three main types of row operations: swapping rows, multiplying a row by a nonzero scalar, and adding or subtracting multiples of one row to another.
2. Row operations are used in Gaussian elimination to transform a matrix into its row echelon form or reduced row echelon form.
3. The determinant of a matrix changes sign when two rows are swapped but remains the same when other row operations are performed.
4. Row operations do not change the solution set of the linear system represented by the matrix.
5. Performing inverse operations can revert the matrix back to its original form.

Review Questions

• What are the three types of elementary row operations?
• How does performing a row swap affect the determinant of a matrix?
• Why are row operations useful in solving systems of linear equations?

Related terms

Gaussian Elimination: A method for solving systems of linear equations by transforming the system's augmented matrix into an upper triangular or row echelon form using row operations.

Reduced Row Echelon Form (RREF): A form of a matrix where each leading entry is $1$, all elements above and below each leading entry are $0$, and each leading entry is to the right of any leading entries in previous rows.

Inverse Matrix: A matrix that, when multiplied with its original matrix, yields the identity matrix. It can be used to solve systems of linear equations.