Question

Given the orthogonal basis B for R4 and the vector v below, find the Fourier coefficients for v with respect to B. Your coefficients should be given in the same order as the vectors in B. B = 1 22 -1 | 7 | 0 | 0 | |-1 | 2 Fourier Coefficients: 0, 0, 0, 0

Answer 1

Given: Be{ų, ą gaun} is an orthogonal basis for Ry ohet a, a, a, au be respectively the ✓ with respect to B. Fourier efficients for Then a = <J,5,7 (3) (1)+(-4)(-2) + (4) (2)+(-1)(-3) u 112 (1) 2+(-2)²+(2)²+(-3)2 = 3 +8 +8+3 a 1+4+4+9 a- <5, üz? – (3) (-1)+(-4) (2)+(4)(7) + (-) (3) - 115,112 (-12+(2)²+(71²+13)² -3-8728-3 = 14 = 32 +4+49+9 63 - 9 ar <5. 2 – (3) (1) + (-4) (2)+(4)(0)+(-1) (-1) 11642 (1) 2+ (2)2+(0)²+(-12 z 3 - 8 tot tutotu ay = <v. Hy> - (3)(4)+(-4)2-1]+(4)(0)+(-1)(3) au- u 112 - K3+(-12+105+(212 12 +4 +o-2 16tltoty .:9,- . 8 = }; 9Şu an}