Question: (a) Suppose A.B are m x n matrices such that ker A = ker B. Prove that there is a nonsingular m m matrix

(a) Suppose A.B are m x n matrices such that ker A = ker B. Prove that there is a nonsingular m × m matrix M such that MA = B.
(b) Use this to conclude that if Ax = b and Bx = c have the same solutions then they are equivalent linear systems, i.e., one can be obtained from the other by a sequence of elementary row operations.

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a Since they have the same kernel their ranks are the same Choose a basis v 1 v n of R n ... View full answer

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