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Re: Question on Matrix Representations as Linear Transformations
Posted:
Apr 24, 2005 9:34 AM
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Thanks a lot.
I am just not certain about the technique you used (I think it's
partially do to the notation we have to use on these boards).
Specifically I am not sure how you formed T_A or T_1 (why is T_A =
(5x_1 + 4x_2, 3x_1 + 6x_2, ?, ?)).
If you could elaborate on this process a little further, I'd appreciate
it.
Paul Sperry wrote:
> In article <1114305774.143369.41210@l41g2000cwc.googlegroups.com>,
> <"verygoodmusic@gmail.com"> wrote:
>
> > Let T1: R4 --> R2 and T2: R2 --> R4.
> >
> > If T1(x1, x2, x3, x4) = (x1, x2) and T2(x1, x2) = (x1, x2, 0, 0)
and
> > Ta: R4 --> R4 be defined by T(x) Ax, where
> >
> > A is 4x4 with the following rows from top to bottom
> > [5 4 -1 9]
> > [3 6 1 5]
> > [5 2 -1 4]
> > [1 -2 -3 5]
> >
> > Find T1 o TA o T2.
> >
> > Thanks.
> >
>
> Adjusting your notation a little: ' means transpose.
>
> T_2((x_1, x_2)') = (x_1, x_2, 0, 0)'.
>
> T_A((x_1, x_2, 0, 0)') = A(x_1, x_2, 0, 0)' =
> (5x_1 + 4x_2, 3x_1 + 6x_2, ?, ?)'.
>
> T_1((5x_1 + 4x_2, 3x_1 + 6x_2, ?, ?)') = (5x_1 + 4x_2, 3x_1 + 6x_2)'
>
> If you would ask the questions from the "Urgent help" thread the way
> you did this one, you would have a lot better luck. I, too, am among
> those who are not willing to download a pdf file; I'm not offended, I
> just won't do it.
>
> --
> Paul Sperry
> Columbia, SC (USA)
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