[Solution] Consider the vector space C([0,2 π]) of continuous real-valued functions on the closed interval [0,2 π], with inner product < f, g>=∫_0^2
Question: Consider the vector space \(C([0,2 \pi])\) of continuous real-valued functions on the closed interval \([0,2 \pi]\), with inner product
\[\langle f, g\rangle=\int_{0}^{2 \pi} f(x) g(x) d x\]Show that the functions \(f(x)=\cos (2 x)\) and \(g(x)=\sin (3 x)\) are orthogonal.
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(Solved) Consider the real inner product space C([0,2 π]),
![[Solution] Consider the vectors v_1=(1,2,3), v_2=(0,1,4), and](/images/solutions/MC-solution-library-72410.jpg "[Solution] Consider the vectors v_1=(1,2,3), v_2=(0,1,4), and")
[Solution] Consider the vectors v_1=(1,2,3), v_2=(0,1,4), and
![[Solution] Equip R^4 with the Euclidean inner](/images/solutions/MC-solution-library-72411.jpg "[Solution] Equip R^4 with the Euclidean inner product (the dot product.)")
[Solution] Equip R^4 with the Euclidean inner product (the dot product.)
![[Solution] Let f: R^2 \rightarrow R^2 be](/images/solutions/MC-solution-library-72412.jpg "[Solution] Let f: R^2 \rightarrow R^2 be defined by (u, v)=f(x,")
[Solution] Let f: R^2 \rightarrow R^2 be defined by (u, v)=f(x,
(See Solution) Show that the equation y^3+x^2 y-2 x^3-x+y=0 defines
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