anonymous
  • anonymous
let v=(1,9,-1,5). find a basis of the subspace of R^4 of all vectors perpendicular to v.
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Perpendicular to v\[ \rightarrow x_1 + 9x_2 -x_3 + x_4 = 0 \rightarrow x_3 = x_1 + 9x_2 + x_4 \] Then by decomposition we have \[\rightarrow \{<1,0,1,0>, <0,1,9,0>, <0,0,1,1>\}\] is a basis of the subspace.

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