I have a couple questions I need help in. I don\'t know what linear transformati

Question

I have a couple questions I need help in. I don't know what linear transformation, inner outer product, etc or anything like that. Please help. I've written out the questions. Please be clear since I have no idea what to do for any of these.

Let A = [-1 0 0 -1], Describe the action of A on an arbitrary vector in R2. Let T:R2 rightarrow R3 be linear, such that Find the matrix of the linear transformation, based on the geometric description. Calculate AB according to the definition also calculating each column according to definition. Calculate AB according to the row-column dt product rule, using Calculate AD and DA. Compare the two results. Find a matrix B such that AB = BA.

Explanation / Answer

Note : the last matrix in 3HW7 (which is a little cut) is just the transpose of uv^T. Sorry for the writting, it was in a hurry, maybe there is typo, but the process should be understandable :-) If you have any question, please ask !

It seems I can't upload image, so here are the uploaded links :

https://www.dropbox.com/s/ngc1rl49q7u2ls5/photo%201.JPG

https://www.dropbox.com/s/lyknq2ielf03m52/photo%202.JPG

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