Linear algebra - coordinates. following, exactly, example, outline

amy

Can anyone explain exactly how you are supposed to apply coodinates in matrices? I am somewhat lost in class.

For example say, i have the coordinates A =
1 2
0 2   --gt; this is a 2 X 2 matrixand I have to apply this to the basis

B =
1 0
0 0,

0 1
0 0,

0 1
0 1-gt; The book gives the following matrix as the answer:

1 0 0
0 1 1
0 0 1

- But I still don't get how they got here. Can anyone outline the process?

Thank you!  

    No, I have no idea what you are talking about.  (And I thought I knew a little about Linear Algebra!)  I have never heard of quot;applying coordinatesquot; to matrices, nor do I see how you are going from 2 by 2 matrices to a 3 by 3 matrix.  Could you state the problem exactly as it is given?  

    I am sorry, this is supposed to be a change of basis problem. We are changing B to basis A.

Can you help?  

    we are trying to find the change of basis matrix.  

    From what basis to what basis?  And what space?  The matrices you list as a basis are NOT a basis for M4, because there are only 3 of them.  

    from B to A. Please help me. The question asks for the change of basis matrix.

No other info is given.  

    Please help me brothers.  

    Honestly, the problem, as you stated it, still makes no sense to me.  You have given us 3 matrices which you say is a basis (of what space? The space of all 2 by 2 matrices is 4 dimensional so it can't have a basis of 3 matrices) and ask for a quot;change of basis matrixquot;.  What is the basis to change to?