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

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[L( \left[\begin{matrix}1 & 0 \\ 0 & 0\end{matrix}\right]) =\left[\begin{matrix}0 & 3 \\ 2 & 4\end{matrix}\right]\] \[L(\left[\begin{matrix}0 & 1 \\ 0 & 0\end{matrix}\right])=\left[\begin{matrix}2 & 3 \\ 0 & 1\end{matrix}\right]\] \[L(\left[\begin{matrix}0 & 0 \\ 1 & 0\end{matrix}\right])=\left[\begin{matrix}0 & 1 \\ 4 & 4\end{matrix}\right]\] \[L(\left[\begin{matrix}0 & 0 \\ 0 & 1\end{matrix}\right])=\left[\begin{matrix}0 & 2 \\ 4 & 4\end{matrix}\right]\]

slaaibak
 4 years ago
Best ResponseYou've already chosen the best response.2\[T(\left[\begin{matrix}a & b \\ c & d\end{matrix}\right]) = \left[\begin{matrix}2b & 3a 3b +d 2d \\ 2a+4c +4d & 4a+b4c4d\end{matrix}\right]\]

slaaibak
 4 years ago
Best ResponseYou've already chosen the best response.2Sorry top right should be: 3a  3b + c 2d T(kernel) = 0 so solve this system: 2b=0 3a  3b + c 2d=0 2a+4c4d=0 4a+b4c4d=0

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0thnks with that i was able to do get to the answer, so nullity = 0 and rank =4 thanks
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