Elementary row operations
Elementary row operations are a set of operations that can be performed on the rows of a matrix in order to transform it into a simpler or more useful form
Elementary row operations are a set of operations that can be performed on the rows of a matrix in order to transform it into a simpler or more useful form. There are three types of elementary row operations:
1. Interchange rows: This operation involves swapping the positions of two rows in a matrix. It is denoted by R(i) <-> R(j), where R(i) represents the ith row and R(j) represents the jth row.
2. Multiply a row by a non-zero scalar: This operation involves multiplying all the elements of a row by a non-zero scalar. It is denoted by k * R(i), where k is the scalar and R(i) represents the ith row.
3. Add a multiple of one row to another row: This operation involves adding a multiple of one row to another row. It is denoted by R(i) + k * R(j), where R(i) represents the ith row, R(j) represents the jth row, and k is a scalar.
These elementary row operations are commonly used in matrix manipulation, particularly in solving systems of linear equations or finding matrix inverses. By applying a sequence of these operations to a matrix, we can transform it into a row echelon form or reduced row echelon form, which makes it easier to analyze and solve mathematical problems.
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