Finn en basis for NulA\operatorname{Nul}ANulA der A=(120−10012)A=\begin{pmatrix}1&2&0&-1\\0&0&1&2\end{pmatrix}A=(102001−12).
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Pivoter i kol 1 og 3; frie variabler x2=s,x4=tx_2=s,x_4=tx2=s,x4=t. Da x1=−2s+t, x3=−2tx_1=-2s+t,\ x_3=-2tx1=−2s+t, x3=−2t. x=s(−2,1,0,0)+t(1,0,−2,1)\mathbf{x}=s(-2,1,0,0)+t(1,0,-2,1)x=s(−2,1,0,0)+t(1,0,−2,1). Basis: {(−2,1,0,0),(1,0,−2,1)}\{(-2,1,0,0),(1,0,-2,1)\}{(−2,1,0,0),(1,0,−2,1)}, dimNulA=2\dim\operatorname{Nul}A=2dimNulA=2.
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