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Show that the setB' = {(1,-1,2,1), (1,1,-4,3),(1,2,0.3), (1,2,-2,0)}basis for R"...

Question

Show that the setB' = {(1,-1,2,1), (1,1,-4,3),(1,2,0.3), (1,2,-2,0)}basis for R"

Show that the set B' = {(1,-1,2,1), (1,1,-4,3),(1,2,0.3), (1,2,-2,0)} basis for R"



Answers

The set $\mathcal{B}=\left\{1+t^{2}, t+t^{2}, 1+2 t+t^{2}\right\}$ is a basis for $\mathbb{P}_{2}$ Find the coordinate vector of $\mathbf{p}(t)=1+4 t+7 t^{2}$ relative to $\mathcal{B} .$


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