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Math Help - Linear Transformations homework help.

  1. #1
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    Linear Transformations homework help.

    Linear Transformations homework help.-hw2.jpg

    1. Scalar multiplication and vector addition are preserved, therefore this is a linear transformation.

    2. Scalar multiplication and addition are preserved, therefore this is a linear transformation.

    3.
    A =
    1 -3 5
    0 1 -1

    4.
    a.
    1 -2
    1 0

    b.
    3 0
    -1 2

    5.
    a. K(T) = [0, 0, x3]
    b. T is not injective because the kernel includes nonzero vectors.
    c. [x2, x1, 0]
    d. T is not surjective because the range does not span the codomain.
    e. T is not invertible.

    Sorry for the poor formatting. Every row vector in problem 5 was originally a column vector. I just need to see if I'm going anywhere in the right direction here. Thanks.
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  2. #2
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    Quote Originally Posted by pantsaregood View Post
    Click image for larger version. 

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    1. Scalar multiplication and vector addition are preserved, therefore this is a linear transformation.

    2. Scalar multiplication and addition are preserved, therefore this is a linear transformation.

    3.
    A =
    1 -3 5
    0 1 -1

    4.
    a.
    1 -2
    1 0

    b.
    3 0
    -1 2

    5.
    a. K(T) = [0, 0, x3]
    b. T is not injective because the kernel includes nonzero vectors.
    c. [x2, x1, 0]
    d. T is not surjective because the range does not span the codomain.
    e. T is not invertible.

    Sorry for the poor formatting. Every row vector in problem 5 was originally a column vector. I just need to see if I'm going anywhere in the right direction here. Thanks.
    It looks pretty fine to me. In 5-(c) I'd simply write \left\{(x,y,0)\in\mathbb{C}^3\right\} , and in 5-(e) I'd write why is T not invertible.

    As for 4 it is almost impossible to check (at least for me) without seeing the actual data and checking. If you want to

    enhance seriously your maths writing go to the LaTeX help section in the forum to learn how to do it.

    Tonio
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