How do you apply coordinates in matrices to change basis?

[frasifrasi]

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 --> this is a 2 X 2 matrix


and I have to apply this to the basis

B =
1 0
0 0,

0 1
0 0,

0 1
0 1


-> 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!

 

[HallsofIvy]

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 "applying coordinates" 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?

 

[frasifrasi]

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

Can you help?

 

[frasifrasi]

we are trying to find the change of basis matrix.

 

[HallsofIvy]

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.

 

[frasifrasi]

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

No other info is given.

 

[frasifrasi]

Please help me brothers.

 

[HallsofIvy]

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 "change of basis matrix". What is the basis to change to?