Find a basis for the subspace of M2,2

  • Thread starter Xingconan
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  • #1
Xingconan
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Homework Statement


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The Attempt at a Solution


I don't really know how to do this, so I hope someone can give some hints or briefly tell me what I should do.
 

Answers and Replies

  • #2
HallsofIvy
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Well, a good start is to write
[tex]\left[\begin{array}{cc}a_{11} & a_{12} \\ a_{21} & a_{22}\end{array}\right]\left[\begin{array}{cc}1 & 0 \\ -1 & -1\end{array}\right]= \left[\begin{array}{cc}-1 & 0 \\ 1 & 1 \end{array}\right][/tex]

Multiply them out and get 4 equations relating a11, a12, a21, and a22. Are those equations independent? If not how many "independent" variables do you have (in other words, how many must you know in order to be able to calculate the others?).
 

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