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 March 14th, 2011, 09:40 AM #1 Member   Joined: Feb 2011 Posts: 58 Thanks: 0 basis change matrices Let $R[x]_{\le 2}$ be the vector space of polynomials of degree at most 2 over $\Re$. Let $e_{1},e_{2},e_{3}$ and $e'_{1},e'_{2},e'_{3}$ be the bases $1,x,x^2$ and $1,(1 - x),(1 + x)^2$ of $R[x]_{\le 2}$. (i) Write down the basis change matrices from basis $e'_{i}$ to basis $e_{i}$ and from basis $e_{i}$ to basis $e'_{i}$ (ii) Use (i) to write the polynomial $3-4x-2x^2$ as a linear combination of $e'_{1},e'_{2},e'_{3}$

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