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I have two possible answers that I came up with for the basis of the column space for the matrix $\begin{bmatrix}2& 4\\ 4 &8\\ 1 & 2\\ 0 &0\end{bmatrix}$ ..

Is it a matrix with the bottom row removed and e1 and e2 added $\begin{bmatrix}2& 0 & 0\\ 4 &1 & 0\\ 1 & 0 & 1\end{bmatrix}$

or does the bottom row stay $\begin{bmatrix}2& 0 & 0 & 0\\ 4 &1 & 0 &0\\ 1 & 0 & 1 & 0\\ 0 & 0 & 0& 1\end{bmatrix}$ ?

user2514676
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  • Question is unclear. Can you explain in details. – DiffeoR Mar 25 '14 at 13:15
  • Basis of a matrix is meaning less. What is the vector space here ? – DiffeoR Mar 25 '14 at 13:17
  • It looks to be R^4 so I guess the last answer is correct. – user2514676 Mar 25 '14 at 13:24
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    It does not make sense to ask for the basis for the matrix. Perhaps, you seek a basis for the column space? or, a basis for the row space? – Brad S. Mar 25 '14 at 13:33
  • @user2514676, you should make a further effort to render a sound question. As for now your question makes no sense at all and it is even hard to understand what you could have meant to ask. Common, this is college/university level, we must strive to be clearer! – DonAntonio Mar 25 '14 at 13:40
  • I'm looking for the basis of the column space – user2514676 Mar 25 '14 at 14:24
  • A basis of a vector space is a set of vectors, not a matrix; while your question now makes sense, neither of your prospective answers is correct (even if you interpret a matrix as determining its set of columns). What's your understanding of a "column space", and of a "basis"? – Andrew D. Hwang Mar 25 '14 at 21:16
  • Getting into lengthy discussions about all the applicable theorems doesn't seem to be the quickest path to answering the original question. My two answers follow the same pattern as other answers for similar problems already given to me. If neither of the two answers I provided are correct, I need to know what the correct answer is. – user2514676 Mar 25 '14 at 23:32

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