Here is a given efficiency matrix, where very row represents different letter (From A to G) and every column gives the value that should be applied on the particular position What I want to do is to create a matrix with values that correspond to the letter and it's position. I have done it like that

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To calculate inverse matrix you need to do the following steps. Set the matrix (must be square) and append the identity matrix of the same dimension to it. Reduce the left matrix to row echelon form using elementary row operations for the whole matrix (including the right one). As a result you will get the inverse calculated on the right.

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This function returns the rank of a square numeric matrix based on the selected method. If the user specifies "qr" as the method, then the QR decomposition function is used to obtain the rank.