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Math Help - linear transformation problem

  1. #1
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    linear transformation problem

    If is a linear transformation such that
    and then



    Let me explain my thinking first:

    so a(1+2x)+b(3+5x) = -2 - 3x

    I solved and got that a = 1 ; b = -1

    I then did:

    1(2-3x) + -1(2-3x) = 0.

    The homework system I'm using only allowed me one try on the problem, and so I want to make sure that I did it correctly, however, my gut tells me 0 is not the right answer. Is my instinct right or am I doubting myself?

    Any help would be greatly appreciated, I only have one attempt and I'd like to get it right!
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  2. #2
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    T(1+2x)=T(3+5x)=-2-3x this is strange!
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  3. #3
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by elven06 View Post
    If is a linear transformation such that
    and then



    Let me explain my thinking first:

    so a(1+2x)+b(3+5x) = -2 - 3x

    I solved and got that a = 1 ; b = -1

    I then did:

    1(2-3x) + -1(2-3x) = 0.

    The homework system I'm using only allowed me one try on the problem, and so I want to make sure that I did it correctly, however, my gut tells me 0 is not the right answer. Is my instinct right or am I doubting myself?

    Any help would be greatly appreciated, I only have one attempt and I'd like to get it right!
    0=T(3+5x)-T(1+2x)=T((3+5x)-(1+2x)))=T(2+3x)=-T(-2-3x)
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  4. #4
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    Quote Originally Posted by Drexel28 View Post
    0=T(3+5x)-T(1+2x)=T((3+5x)-(1+2x)))=T(2+3x)=-T(-2-3x)
    wait so that would equal 2+3x then?
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  5. #5
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    Quote Originally Posted by elven06 View Post
    If is a linear transformation such that
    and then



    Let me explain my thinking first:

    so a(1+2x)+b(3+5x) = -2 - 3x
    No, it is 2- 3x, not -2- 3x, that you want to apply T to. You want to find a and b such that a(1+ 2x)+ b(3+ 5x)= 2- 3x.

    Once you have done that, T(2- 3x)= T(a(1+2x)+ b(3+ 5x))= aT(1+2x)+ bT(3+ 5x)= a(-2-3x)+ b(-2-3x).

    Are you sure you have copied this correctly. It seems peculiar that T(1+2x) and T(3+ 5x) are exactly the same (though possible, of course).

    I solved and got that a = 1 ; b = -1

    I then did:

    1(2-3x) + -1(2-3x) = 0.

    The homework system I'm using only allowed me one try on the problem, and so I want to make sure that I did it correctly, however, my gut tells me 0 is not the right answer. Is my instinct right or am I doubting myself?

    Any help would be greatly appreciated, I only have one attempt and I'd like to get it right!
    Follow Math Help Forum on Facebook and Google+

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