# Answer to Question #24292 in Linear Algebra for Jacob Milne

Question #24292

Prove that if A is M by N and M<N, then there is a non-zero x with Ax = 0.

Expert's answer

Every solution of Ax=0 is thesolution to Bx=0, where B is row echelon form, j=rankA=rankB. For B we have n-j

last zero rows, and these corresponding x_i 's can be choosen linearly

independent, and other will be automatically computed, so there will be n-j linearly

independent solutions.

So, choosing last coordinate one will obtain nonzero solution.

last zero rows, and these corresponding x_i 's can be choosen linearly

independent, and other will be automatically computed, so there will be n-j linearly

independent solutions.

So, choosing last coordinate one will obtain nonzero solution.

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