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Calculate a)Explicitly display, if any, an inner product (: )) in R2 under which the vectors f, =(1,1) and f 2 =(1,2) are orthogonal. (b) If w it is a vector in R² such that ((S1, w)) = -1 and ((S2, w)) = 3 find w. Note: the internal product (,) considered here must be the same obtained in item (a). c)Calculate the Fourier coefficients of the vector (-1.3) with respect to the ortho base normal obtained from the vectors fi and fa. considering the internal product found in item (a).

Calculate a)Explicitly display, if any, an inner product (: )) in R2 under which the vectors f, =(1,1) and f 2 =(1,2) are orthogonal. (b) If w it is a vector in R² such that ((S1, w)) = -1 and ((S2, w)) = 3 find w. Note: the internal product (,) considered here must be the same obtained in item (a). c)Calculate the Fourier coefficients of the vector (-1.3) with respect to the ortho base normal obtained from the vectors fi and fa. considering the internal product found in item (a).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Calculate a)Explicitly display, if any, an inner product (: )) in R2 under which the vectors f; =(1,1) and f 2 =(1,2) are orthogonal. (b) If w it is a vector in R2 such that ((f1, w)) = -1 and (f2, w)) = 3 find w. Note: the internal product (,) considered here must be the same obtained in item (a). C)Calculate the Fourier coefficients of the vector (-1.3) with respect to the ortho base normal obtained from the vectors fi and fa. considering the internal product found in item (a). edited question
Transcribed Image Text:Calculate a)Explicitly display, if any, an inner product (: )) in R2 under which the vectors f; =(1,1) and f 2 =(1,2) are orthogonal. (b) If w it is a vector in R2 such that ((f1, w)) = -1 and (f2, w)) = 3 find w. Note: the internal product (,) considered here must be the same obtained in item (a). C)Calculate the Fourier coefficients of the vector (-1.3) with respect to the ortho base normal obtained from the vectors fi and fa. considering the internal product found in item (a). edited question
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