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Math Help - V,W have basis and dim(null(t))

  1. #1
    jax
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    V,W have basis and dim(null(t))

    Hello, I can't seem to figure out this problem about linear maps:

    Assume v1,v2,..v5 is a basis of V and w1,w1,...w6 is a basis of W. Suppose you need to define a linear map T: V --> W. Which values would you assign to T(v1),T(v2),..T(v5) if it is required that dim(Null(T))=3, and that w1 is not in range(T).

    I was wondering if the values of T(v1),..T(v5) should be scalars, or be variables with respect to w.

    Thank you!!
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  2. #2
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    Quote Originally Posted by jax View Post
    Hello, I can't seem to figure out this problem about linear maps:

    Assume v1,v2,..v5 is a basis of V and w1,w1,...w6 is a basis of W. Suppose you need to define a linear map T: V --> W. Which values would you assign to T(v1),T(v2),..T(v5) if it is required that dim(Null(T))=3, and that w1 is not in range(T).

    I was wondering if the values of T(v1),..T(v5) should be scalars, or be variables with respect to w.

    Thank you!!
    ??? You just said, T is a linear map from V to W. No, T(v1), etc. are NOT numbers, nor are they "variables with respect to W" (whatever that might mean). T(v1) etc. are vectors in W. That' is exactly what "T is a linear map from V to W" means.
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  3. #3
    jax
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    I found the answer and actually they were numbers and vectors with respect to w. So you were wrong, but thanks anyways

    T(v1)=0
    t(v2)=0
    t(v3)=0
    t(v4)=w2+w3
    t(v5)=w4+w5+w6
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