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mathwizarddud
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Prove that a matrix A is invertible if and only if its reduced row echelon row is the identity matrix.
The purpose of transforming a matrix to RREF is to simplify the matrix and make it easier to perform calculations on it. It also helps to identify important properties of the matrix, such as its rank and invertibility.
A matrix is invertible if and only if its RREF form is the identity matrix. In other words, if all the leading entries in each row are 1 and all other entries in the same column are 0, then the matrix is invertible.
No, a non-square matrix cannot be invertible. In order to be invertible, a matrix must have the same number of rows and columns.
The inverse of a matrix is closely related to its RREF form. The inverse is found by performing the same row operations on the identity matrix that were used to transform the original matrix to RREF.
Knowing if a matrix is invertible is important because it allows us to solve equations and perform other calculations involving that matrix. Invertible matrices have many useful properties and are essential in many areas of mathematics and science.