5. Let w = i.$= (4.2+3.4.2-2w). 1 = (1.3w. 20.-w). Find the point wise multiplication ext.
numerical analysis problem 4. Let s = (2,1, -4,3). Find the discrete Fourier transform F(s) of s. 5. Let w=i, s = (1, 2+2w, 3, 2-2w), t = (4,3w, 2w, -w). Find the pointwise multiplication ext.
20 3. Let 1 = 2 and = 5. Let W = Span{11, 13). (a) Give a geometric description of W. (b) Use the Gram-Schmidt process to find an orthogonal basis for W. (c) Let = 2 Find the closest point to į in W. (a) Use your orthogonal basis in part (b) to find an orthonormal basis for W.
3. If signal 13(t) has Fourier transform J 1-2W, -0.5 <w< 0.5 otherwise 0 find 13t).
5.57 Let np(t) be a zero-mean white Gaussian noise with the power spectral density 20 let this noise be passed through an ideal bandpass filter with the bandwidth 2W centered at the frequency fe. Denote the output process by nt). 1. Assuming fo fe, find the power content of the in-phase and quadrature components of n(t). We were unable to transcribe this image 5.57 Let np(t) be a zero-mean white Gaussian noise with the power spectral density 20 let this...
V W | | Let A-(as)- | ↓ ↓ -5 2. Let v and w - I be the 3 2 matrix whose columns are v and w and let B - (b; - be the 2 x 3 matrix whose 1 WT → rows are v1 and w1. Find a1, a13, a21, b32, bi2, and b22 if possible
2. Let v= [6, 1, 2], w = [5,0, 3), and P= (9, -7,31). (i) Find a vector u orthogonal to both v and w. (ii) Let L be the line in R3 that passes through the point P and is perpendicular to both of the vectors v and w. Find an equation for the line L in vector form. (iii) Find parametric equations for the line L.
Problem 9. (1 point) T -5 10 1 Let A= and w= 2 -4 Is w in Col(A)? Type "yes" or "no". Is w in Nul(A)? Type "yes" or "no". Note: You can earn partial credit on this problem.
37 Let u=8i - 8j, and w=-i-2j. Find ||w-ul. w-ul=1 (Type an exact answer, using radicals as needed.) Let u=8i - 8j, and w=-i-2j. Find ||w-ul. ||w-ul=1 (Type an exact answer, using radicals as needed.)
Question 3 [10 marks Let W Then the p.d.f. 1 fw (w) 2"/21 (n/2) exp(-w/2) w3-1, w>0. and the c.d.f. is denoted as Fw (w) (a) Show that 0, n > 0, and (i) The function fw(w) is a p.d.f. (i.e., that fw(w) 2 0 for w Jo fw(w)dw 1). (ii) The mode of W is n - 2 for n > 2. (b) As n oo, W becomes normally distributed with mean n and variance 2n. This has led...
(1 point) Let u = 1. VE L . and let W the subspace of R4 spanned by {u, v}. Find a basis for WI. Answer: