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Mathematics
Linear and Abstract Algebra
11.1 Determine if the polynominal.... is the span of (....,....)
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[QUOTE="Olinguito, post: 6775635, member: 715504"] [FONT=Times New Roman][SIZE=4]That solution is for the problem of determining if this polynomial $$2x^2+x+1$$ is in $\mathrm{Span}\{x^2+x,x^2-1,x+1\}$. In your OP, you have this: $$c_1(x^2+x-1)+c_2(x^2-x+2)+c_3\ \equiv\ 3x^2+2x-1$$ so comparing coefficients of $x^2$, $x$ and the constant terms should give you $$\begin{array}{rcrcrcr}c_1 & +&c_2 && &=& 3 \\ c_1 &-&c_2 && &=& 2 \\ c_1 &+&2c_2 &+&c_3 &=& -1\end{array}.$$[/SIZE][/FONT] [/QUOTE]
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Mathematics
Linear and Abstract Algebra
11.1 Determine if the polynominal.... is the span of (....,....)
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