Fon each of the following matrice A, compute the SVD, the spectral A(1) Смол morm ||All 2. The nark-1 approximation  (2), and the approximation ennen ||A -  (1)||2, where || 112 is the spectral ci A = 322 23 23-2 22 A-[11] (ii) A = (iii) A= 1 norm: Make sure to keep the exact nadicals and do not round
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- Compute using Lagrange Inerpolation f(-0.016) for the data (-1.5, - 14.1014), (-0.75, - 0.931596), (0,0), (0.75 , 0.93 1596), (1.5, 14.1014) .a The answer is not included in the options .b 0.02367 .C 0.02362 .d 0.02366 .e 0.02361 .f 0.02365 .g 0.02364 .h 0.02363 .i 0.02369 j 0.02368Let φ1(x) = 1, φ2(x) = x/|x|, φ3(x) = x^2 − 1/3 for −1 ≤x ≤1.Show that (φ1,φ2,φ3) form an orthogonal set.Let f be defined by the graph to the right. Find VK0.3)+ 1(1.1) - *)° + (-1)+1(2)-1(-*) VO 3) - 1(1.1) – 1(x)}² + (-1) - 1(2) • 1( – 2) = 0
- Find the Wronskians of the given sets of functions and determine whether the functions are linearly independent on dependent. a. (x^2 , x^3 x,^4) b. (sin x, 2 cos x, 3 sin x+cos x)let be a defferentlable function such thal gand g take the following values. ge/3)=1, g(1/3) = Q, g(2)= 2, g(2)=4 eompute fr/3) up f6)=g6) Since) B Compute hi@) 4 h@= Vi+ag6)Let à = ст -5' -4 Find ||a, the norm of a.
- 6.1.2 Consider the following subintervals of the real line: A = [2,5), В 3 (0,4). (a) Express the set (A \ B)C in interval notation, as a disjoint union of intervals. (b) Draw a picture of the set (A\ B)C × (B \ A).Let S = (0, x), T = (-∞, 2], and W = [-4, 2). For each intersection or union, choose the correct notation for the resulting interval from the list below. (a) TnW = Choose v (b) SUT = Choose v (c) SnW = Choose v (d) SNT = Choose v C = [-4, 2) F = (-0, 2] A = (0, 2] B= (0, 2) D = (-00, 0) E = [-4, 0)Let f (x) C = C = = x on [0, 5], and let P = {0, c, 5}. Find two values of c in (0, 5) such that Uf (P) = 22. (smaller value) (larger value)
- Suppose that A(x) =B(x)Rα(x)f(u)du. Use sweeping to find ddxB(x)Rα(x)f(u)du. You may use x as the time andα(x) and B(x) as the respective position function of the moving left and right vertical segments.10. Consider an FNN with two hidden layers. There are p = 4 input units, 2 units in the first. hidden layer, 3 units in the second hidden layer, and a single output. (a) Draw the model. (b) Write out an expression for f(x), assuming ReLU activation functions for the hidden layers and no activation of the output layer. Be as explicit as you can. (c) How many parameters are there in the model?The normal modes of a fixed string which is plucked or struck are given by Select one: a. O b. C. cos (f,x), with f = nf/L, n = 1, 2, 3 ... cos (knx), with k, = n/L, n = 1, 2, 3 ... sin (knx), with f=nf /L, n = 1, 2, 3 d. sin (knx), with k = n/L, n = 1, 2, 3 ...