owlet
  • owlet
I need to understand how to solve questions like this: Find a basis for the range and a basis for the nullspace of the following linear mapping: \(\sf L(x_1,x_2,x_3)=(2x_1, -x_2+2x_3)\) I understand a little bit of nullspace, but i'm still not sure about the range of linear mapping.
Mathematics
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
owlet
  • owlet
@Nnesha @jim_thompson5910 @jigglypuff314
jigglypuff314
  • jigglypuff314
@zepdrix
amistre64
  • amistre64
\[\begin{pmatrix}2&0&0\\0&-1&2\end{pmatrix}\begin{pmatrix}x_1\\x_2\\x_3\end{pmatrix}=\begin{pmatrix}2x_1\\-x_2+2x_3\end{pmatrix}\]

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amistre64
  • amistre64
given Ax=b the columns of A, span the range ... and a basis consists of all the independant column vectors
amistre64
  • amistre64
the basis for the null set, is determined by the solutions to: \[\begin{pmatrix}2&0&0\\0&-1&2\end{pmatrix}\begin{pmatrix}x_1\\x_2\\x_3\end{pmatrix}=\begin{pmatrix}2x_1\color{red}{=0}\\-x_2+2x_3\color{red}{=0}\end{pmatrix}\]

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