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Tom Salazar
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1. Get A from its inverse
3. I believe it has something to do with the theorem that states: E1E2E3...EkA=I
fzero said:
A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. It is commonly used in mathematics, physics, engineering, and other fields to represent and manipulate data.
An elementary matrix is a square matrix that represents a single elementary row operation. These operations include multiplying a row by a non-zero constant, interchanging two rows, and adding a multiple of one row to another.
Matrix A can be obtained from a series of elementary matrices by multiplying them in the same order that the row operations were performed on the original matrix. This results in a new matrix that is equivalent to A.
Using elementary matrices allows for easier manipulation and calculation of matrices, especially when dealing with larger matrices. It also allows for a clear and systematic approach to solving systems of linear equations and finding inverse matrices.
No, elementary matrices can only be used to obtain matrix A if it is possible to reach A from the original matrix through a series of elementary row operations. If the original matrix is not row equivalent to A, then elementary matrices cannot be used to obtain A.