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Math Help - linear map question

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    linear map question

    If T : R^2 -----> R^2 is a linear map defined by T(a,b)=(a+b,a-b)

    what is the matrix of T:

    1) using the standard basis of R^2?

    2) using the basis (-1,1),(0,-2) of R^2
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    Quote Originally Posted by maximus101 View Post
    If T : R^2 -----> R^2 is a linear map defined by T(a,b)=(a+b,a-b)

    what is the matrix of T:

    1) using the standard basis of R^2?

    2) using the basis (-1,1),(0,-2) of R^2
    Using the standard basis

    e_1=(1,0), e_2=(0,1) Then

    T(e_1)=(1,1)=e_1+e_2 and
    T(e_2)=(1,-1)=e_1-e_2

    Remember that the transform of the basis vectors becomes the columns in the matrix representation.

    This gives the standard matrix as

    \begin{bmatrix} 1 & 1 \\ 1 & -1\end{bmatrix}

    2 is exactly the same just use the basis given instead of the standard one.
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