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Thread: Vector space exercise

  1. #1
    Jun 2009

    Vector space exercise

    HI! friends i need help to solve this exercise, i don't know how to do, so help me please!!:

    A) V1 & V2 two vector spaces $\displaystyle V_2=<(2,-1,0,1),(1,-1,3,7)>$ and $\displaystyle V_1=\left\{\begin{array}{cc} x_1-2x_2+3x_3=0
    \\ x_2-2x_3+x_4=0\end{array}\right.
    Determine the basis for: $\displaystyle V_1\cap V_2$ y $\displaystyle V_1+V_2$.

    B) From the base standard, determine the matrix of endomorphic $\displaystyle T$ characterized by verifying:

    1-$\displaystyle KerT$ (core of $\displaystyle T$) is the space vector defined by the equations:

    $\displaystyle KerT=\left\{\begin{array}{cc} x+y+z=0
    \\ 2x-y=0\end{array}\right.

    2-$\displaystyle (1,0,1)$ y $\displaystyle (2,1,-1)$ are eigenvectors of eigenvalues 1 and 2, respectively.

    Many thanks
    Last edited by vrcatc; Jun 24th 2009 at 06:39 AM.
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