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edpinho

  • 3 years ago

let L be a linear transformation defined by (see inside) Determine the dimention of kernel of L.

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  1. edpinho
    • 3 years ago
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    \[L( \left[\begin{matrix}1 & 0 \\ 0 & 0\end{matrix}\right]) =\left[\begin{matrix}0 & -3 \\ -2 & -4\end{matrix}\right]\] \[L(\left[\begin{matrix}0 & 1 \\ 0 & 0\end{matrix}\right])=\left[\begin{matrix}-2 & -3 \\ 0 & 1\end{matrix}\right]\] \[L(\left[\begin{matrix}0 & 0 \\ 1 & 0\end{matrix}\right])=\left[\begin{matrix}0 & 1 \\ 4 & -4\end{matrix}\right]\] \[L(\left[\begin{matrix}0 & 0 \\ 0 & 1\end{matrix}\right])=\left[\begin{matrix}0 & -2 \\ 4 & -4\end{matrix}\right]\]

  2. slaaibak
    • 3 years ago
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    \[T(\left[\begin{matrix}a & b \\ c & d\end{matrix}\right]) = \left[\begin{matrix}-2b & -3a -3b +d -2d \\ -2a+4c +4d & -4a+b-4c-4d\end{matrix}\right]\]

  3. slaaibak
    • 3 years ago
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    Sorry top right should be: -3a - 3b + c -2d T(kernel) = 0 so solve this system: -2b=0 -3a - 3b + c -2d=0 -2a+4c-4d=0 -4a+b-4c-4d=0

  4. edpinho
    • 3 years ago
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    thnks with that i was able to do get to the answer, so nullity = 0 and rank =4 thanks

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