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Procedure for orking out the basis of the kernel of a linear transformation.

  1. Apr 19, 2012 #1
    I am working on a problem dealing with transformations of a vector and finding the basis of its kernel. Now I have worked out everything below but after reading the definitions I am a bit confused, hence just want verification if the procedure I am following is correct.

    My transformed matrix is given below (R4->R2)

    \begin{bmatrix}3 & 1 & 2 & -1 \\2 & 4 & 1 & -1 \end{bmatrix}

    Reducing to RREF

    \begin{bmatrix}1 & 0 & 7/10 & -3/10 \\0 & 1 & -1/10 & -1/10 \end{bmatrix}

    Now I equal these to zero as I want to work out the kernel as given in the definition of kernel.

    Then the equations can be read out and written in "vector parametric form" as(I thinks that's what its called).

    {\begin{bmatrix}-7/10 \\ 1/10 \\ 1 \\ 0 \end{bmatrix}, \begin{bmatrix}3/10 \\ 1/10 \\ 0 \\ 1 \end{bmatrix}}

    ^^ The 2 matrices above form a set for the basis of the kernel of the transformation right ?
    Last edited: Apr 19, 2012
  2. jcsd
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