## edpinho 2 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

$L( \left[\begin{matrix}1 & 0 \\ 0 & 0\end{matrix}\right]) =\left[\begin{matrix}0 & -3 \\ -2 & -4\end{matrix}\right]$ $L(\left[\begin{matrix}0 & 1 \\ 0 & 0\end{matrix}\right])=\left[\begin{matrix}-2 & -3 \\ 0 & 1\end{matrix}\right]$ $L(\left[\begin{matrix}0 & 0 \\ 1 & 0\end{matrix}\right])=\left[\begin{matrix}0 & 1 \\ 4 & -4\end{matrix}\right]$ $L(\left[\begin{matrix}0 & 0 \\ 0 & 1\end{matrix}\right])=\left[\begin{matrix}0 & -2 \\ 4 & -4\end{matrix}\right]$

2. slaaibak

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

3. slaaibak

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

thnks with that i was able to do get to the answer, so nullity = 0 and rank =4 thanks