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(Solved):
The set \( S=\left\{x^{2}+4,2 x-5,5 x\right\} \) is a basis for \( P_{2} \). Write \( t(x)=6 x^{2} ...
The set \( S=\left\{x^{2}+4,2 x-5,5 x\right\} \) is a basis for \( P_{2} \). Write \( t(x)=6 x^{2}-4 x+9 \) as a linear combination of the elements in basis \( S \). \( t(x)=a \cdot\left(x^{2}+4\right)+b \cdot(2 x-5)+c \cdot(5 x) \) where \[ a=\quad b=\quad c= \]