key term - Row operations

Definition

Row operations are procedures used to manipulate the rows of a matrix in order to solve systems of equations. They include row swapping, multiplying a row by a non-zero scalar, and adding or subtracting multiples of rows.

5 Must Know Facts For Your Next Test

1. There are three types of row operations: row swapping, scaling rows, and adding/subtracting multiples of rows.
2. Row operations are fundamental in Gaussian Elimination for transforming a matrix into Row Echelon Form (REF) or Reduced Row Echelon Form (RREF).
3. Performing row operations does not change the solution set of the system of equations represented by the matrix.
4. When using row operations to find the inverse of a matrix, you append the identity matrix to it and perform row operations until the original matrix becomes the identity matrix.
5. Row operations can be applied step-by-step to simplify complex systems into more manageable forms that can be solved using back-substitution.

Review Questions

Related terms

Gaussian Elimination:

A method for solving systems of linear equations by transforming the system's augmented matrix into Row Echelon Form using row operations.

Inverse Matrix:

A square matrix that, when multiplied by its original matrix, results in an identity matrix. It is found using row operations.

Row Echelon Form (REF): A form of a matrix where all non-zero rows are above any rows of all zeros, and each leading entry is to the right of the leading entry in the previous row.