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Let B = [ aij ] 20×17 be a matrix with real entries. Let x be...

Let B = [ aij ] 20×17 be a matrix with real entries. Let x be in R 17 , c be in R 20, and 0 be the vector with all zero entries. Show that each of the following statements implies the other.

(a) Bx = 0 has only the trivial solution x = 0 n R 17, then (b) If Bx = c has a solution for some vector c in R 20, then the solution is unique.

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