Checking invertiblity of a symbolic matrix (small size N=12)
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I have a symbolic matrix A of size 12x12. I need to check if inverse of this matrix exists. If rank(A)=12, then I know that I can invert it. However, as explained in the official documentation of mathworks, this is not always correct. Another approach is to compute row reduced echelon form of A i.e. rref(A) and check if it is rref(A)=I (identity matrix) to ensure invertibility. If I use a symbolic A and found rref(A)=I,can the invertibilty be guaranteed?
(I can evaluate the matrix A numerically and check invertibility however I don't want to do it for possible cases)
Thanks in advance
JESUS DAVID ARIZA ROYETH el 30 de Jul. de 2020
remember that a matrix has an inverse if and only if its determinant is different from 0, therefore you must calculate for which conditions the determinant of A "det(A)" is different from 0, if it is true for whatever the value of your variables, then that symbolic matrix will always be invertible.