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ichigo444
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Is row echelon form an upper triangular matrix? if so, does this mean that its determinant could be 1 or 0? Even if its row equivalent has a different determinant? Please Answer and thanks.
Row echelon form is a way to represent a matrix in which the leading coefficient of each row is to the right of the leading coefficient of the row above it. It is a useful tool in solving systems of linear equations.
Reduced row echelon form is a stricter version of row echelon form in which the leading coefficient of each row is also the only non-zero entry in its column. This form is useful for finding the solution to a system of linear equations.
The main purpose of using row echelon form is to simplify matrices and make it easier to solve systems of linear equations. It can also help to identify important properties of a matrix, such as its rank and determinant.
To convert a matrix into row echelon form, you can use elementary row operations such as swapping rows, multiplying a row by a non-zero constant, and adding a multiple of one row to another. The goal is to get the matrix into a triangular form with leading coefficients in each row.
Not all matrices can be converted into row echelon form. Matrices that have a row of all zeros cannot be converted, as well as matrices that have a leading coefficient of 0 in a row below a non-zero leading coefficient. Additionally, matrices with more columns than rows cannot be converted into row echelon form.