Let Ax c be a linear equation system with A a nonsingular square n n matrix (rank A n) For every c n there exists a unique solution x (x1, x2, , xn) given by where is the matrix obtained by replacing the jth column of A with c

Question: Let Ax = c be a linear equation system with A a nonsingular square n n matrix (rank A = n). For every c

Let Ax = c be a linear equation system with A a nonsingular square n × n matrix (rank A = n). For every c ∈ ℜn there exists a unique solution x = (x1, x2,..., xn) given by

where

is the matrix obtained by replacing the jth column of A with c.

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