Overview
Row reduction is a fundamental technique in linear algebra that simplifies matrices to make solving systems of linear equations more manageable. By transforming matrices into row echelon form or reduced row echelon form, students can easily apply back substitution to find solutions. This method is n...
Key Terms
Example: A 2x3 matrix has 2 rows and 3 columns.
Example: In row echelon form, the leading coefficient of a non-zero row is always to the right of the leading coefficient of the previous row.
Example: The matrix [[1, 0, 2], [0, 1, -1]] is in reduced row echelon form.
Example: Using Gaussian elimination, we can solve the equations represented by the matrix.
Example: Pivoting helps avoid division by zero in Gaussian elimination.
Example: In the row [0, 0, 1, 2], the leading coefficient is 1.