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Dekoyl's Questions

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enwiabe:
Well, that's wrong, because R3 in and of itself does not imply infinitely many solutions.

I'd say "more unknowns than equations, therefore infinitely many solutions"

dekoyl:
Ah okay thanks - bad example I did there :P
So I have to draw up another matrix to prove my solution, right? Because I think my teacher said there was another way of setting out the answer.

Mao:
that is the way, though your reasoning is wrong. Consider these two matrices:

and

In both cases, the last row is consisted of zeroes, but that is insufficient to say there are infinite number of solutions [in the second matrix it clearly had a distinct solution]. The key is leading entries, when a column does not have a leading entry, it is unbounded and hence there are infinite number of solutions.


but yes, to show that your 'k' value is correct, substitute back in and show the ref with (i) columns w/o leading entry or (ii) [0 0 0 ... | *]

enwiabe:
Mao's answer is more rigorous, re: terminology.

dekoyl:
Is this right for linear mapping? I might've copied the notes wrong.
If , the line transforms to:






Should it be instead of the I did above?




Also:
In 2D, is a dilation by a factor of   from the y-axis or from the y-axix or by a factor of from the x-axis?

Yes I'm still trying to understand some concepts :p

Thanks

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