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If $\mathbb{R}^n=\operatorname{span}\{X_1,X_2,...,X_k\}$ and $A$ is an $m\times n$ matrix, does $AX_i$ not equal $0$ for some $i$?

I think the answer might be no. But when I tried to prove it, I notice the way I did is not so persuasive. Can anybody help?

  • 1
    Are there any conditions on $A$?2012-01-27
  • 0
    NO, just an m*n matrix.2012-01-27
  • 2
    Do you know of any $m \times n$ matrices that send everything to zero?2012-01-27
  • 0
    Do you mean 0 matrix? This question would be meaningless if A is 0 matrix.2012-01-27

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