Practice Problem 17.2 Determine the Fourier series of the sawtooth waveform in Fig. 17.9. 3 3 Answer: f(1) =:-- sin 2 7 nt. -2 -1 0 I 2 3 Figure 17.9 For Practice Prob. 17.2. S0 = a, + E (a, cos narot + b, sin not) f) dt f) sin nat dt|| a. fi) cos neof dt

Q: Find AB such that [3 1 21 T-1 A = 2 1 2 and B =|4 [1 2 2] -2 -5]

A: The solution is given as

Q: Let A = {1,{2,3}}. Find P(A), n(A) and n (P(A)).

A: The power set of a set is the set of its subsets. The expression nA represents the number of…

Q: LetP(A) = 0.10, P(B) = 0.20, and P(A∩B) = 0.02. Are A and B mutually exclusive? Justify your result…

A:

Q: A certain allergen affects approximately 3 people per 10,000 in the United States. Assuming the U.S.…

A: Since the number of people affected per 10, 000 =3  so , if there is only one person then chance of…

Q: L[sih bt) 2.

A: From the definition of Laplace, L(f(t))=Fs=∫0∞fte-stdtSo,L(sin(bt))=∫0∞sin(bt)e-stdt Let,…

Q: 15. Prove: If a, b, c, a, and M are constants and M = 0 then ax²y" + bxy' + cy has a particular…

A: Let us solve above problems.

Q: Let_Z1 = 3 + i and Z2 = 5 + 2 i . Find 2 Z1 /( Z1 - Z2) - (14/5)-2 i O (14/5) + 2i O - (14 / 5) + (…

A: Topic = Complex number

Q: Let a = (1,2, 3), b = (1,0, –1) and c = (2, 1, 3). (a) Verify that a · (2 b+c) =2(a · b) + (a · c).

A: a=(1,2,3) , b=(1,0,-1) and c=(2,1,3)

Q: (d) Develop an estimated regression equation for the data of the form ý = b, + b,x + b,x. (Round b,…

A: e) Consider the following table for necessary calculations. y x x2 12 22 484 22…

Q: Let A = (-0,0), B=(0,0) then AUB=

A:

Q: Show that the equation (1, 2, 3) × v = (−1, 2, a) has no solutionfor a = −1

A: Consider the given: Given equation:1,2,3×v=−1,2,aLet v=x,y,z1,2,3×v=ijk123xyz…

Q: Prove c (A + B) = cA + cB   (c + d)A = cA + dA   c(dA) = (cd)A  IA= A

A:

Q: What’s (E∩F)×(F∪G)

A: We are given that E = {1, 2}, F = {2, 3} and G = {3, 4}.Now, E∩F = {2} and F∪G = {2, 3, 4}.

Q: If x=y+qp and f=xy+qp² Express x in terms of q,p and f

A:

Q: If Cov(Xm, Xn) = mn − (m + n), find Cov(X1 + X2, X3 + X4).

A:

Q: Find u x v, v x u, and v x v. u = (-6, 2, -7) v = (-2,-5, -3) (a) ux v (b) vxu (c) vxv

A: given vectors

Q: Find the sum of the series. e -8x² Σ (−1)n 87x6n n = 0 n! X

A:

Q: Find (a) u − v, (b) 2(u + 3v), and (c) 2v − u. u = (−7, 0, 0, 0, 9), v = (2, −3, −2, 3, 3)

A: a). b).

Q: Find u x v, v x u, and v x v. | = (−1, 5, 4) v = (-5, -4, -7)

A:

Q: Show that (a + b)x = ax + bx for all a, b E F and all x € F¹.

A:

Q: Prove Equationally that A → BF¬B → ¬A.

A: let us check whether the given statement is true or not

Q: Find u x v, v x u, and v x v. u = (3, -3, -1) v = (-2, –7, -5) (a) ux v

A:

Q: Let a = [1, -3, 5], b = [4, 0, 8], c = [-2, 9, 1]. Find: |a + c² + |a − c|² - 2(|a|² + |c|²)

A:

Q: Let w = (2, −2, 1) and v = (4, 5, −4). Solve for u if v + 5u =3w − u.

A: Simplification of the function helps to find the vector u. Component-wise operations help to get…

Q: L{t(u0 – u1) + t²u1}.

A:

Q: Use the Cayley-Hamilton theorem to find constants a, b 5 (-2 and c such that A4= aA² + bA + cl if A…

A: In linear algebra, the Cayley–Hamilton theorem states that every square matrix over a commutative…

Q: Show that (AB)T and BTAT are equal.

A: Now,

Q: LetP(A) = 0.20, P(B) = 0.80, andP(A∩B) = 0.16. Are A and B independent? Justify your result…

A:

Q: Find u x v, v x u, and v x v.

A:

Q: Let P (x) = 2x - 15a + az?+ bx + c, where a, %3D Given that (x - 5) is a factor of P (r), find a…

A: It is given that,  P(x) = 2x4 - 15x3 + ax2 + bx + c It is given that, (x - 5) is a factor of P(x).

Q: If Cov(X,Y) = 0, then Var(X+Y) = Var(X-Y). True or False? O True

A: Given that, COVX,Y=0