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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 V_2=<(2,-1,0,1),(1,-1,3,7)> and V_1=\left\{\begin{array}{cc} x_1-2x_2+3x_3=0<br />
\\ x_2-2x_3+x_4=0\end{array}\right.<br />
    Determine the basis for:  V_1\cap V_2 y V_1+V_2.

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

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

    KerT=\left\{\begin{array}{cc} x+y+z=0<br />
\\ 2x-y=0\end{array}\right.<br />

    2- (1,0,1) y (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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