- #1
kostoglotov
- 234
- 6
Moved from a technical forum, so homework template missing.
imgur link: http://i.imgur.com/fieHb7f.png
imgur link: http://i.imgur.com/UpDPZ6K.jpg
Solution:
imgur link: http://i.imgur.com/gUHCb1u.png
I can see that [itex]A^+A[/itex] and [itex]AA^+[/itex] are matrices that project onto the column and row space respectively.
But
(i) where does the [itex]A^+[/itex] figure into the calculation, because those answers are not A matrix-multiplied by [itex]A^+[/itex] or [itex]A^+[/itex] matrix-multiplied by A?
(ii) if [itex]A^+[/itex] isn't used to find the last two answers, why calculate it in the first place, what purpose does it serve? I could just find the column and row space basis vectors by other methods and construct those last two answers accordingly.
(iii) why are those answers given in the form that they are? wouldn't [itex]A^+A[/itex] be just as good given as
[tex]A^+A = \begin{bmatrix}1 & 2\\2 & 4\end{bmatrix}[/tex] ?