[2 0] [26] For A = 1 3 and b = , a least-squares solution of Ax = bis 3 1 5 What is the least-squares error associated with this solution? 3

Q: Question 2 3 Cansider the arthagonal basis B: of R 5 Let U = -64 15 If [v]B = 6|. what is the value…

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Q: n=1 Vn + termine the radius and interval of convergence of the power series. termine the largest…

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Q: Find the particular solution of

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Q: 1 37 a Let A 1 1 Find a QR-factorization of A. If R = then the 1 value of a is , the value of b is…

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Q: Consider the inner product space (P2, (, )) with the inner product (p(t), q(t)) =…

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Q: Question 24 If A = (aji) is the matrix of the quadratic form a? + 2x% + 2x3 + 6¤1x2 – 22x13 – 8x2x3,…

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Q: Find all integer solutions (if any) of the following Diophanti- ne equations. 1. 43x+64y = 1

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Q: Let T : R? → R´be defined by [2 _5||X1 X2 1 6] [x2] а If B = is a basis for R“ such that |T'|B is a…

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Q: 4. Find the solution of the system of linear equation a) By Matrix Inversion b) By Cramer's Rule 2x…

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Q: EXERCISES 2: Find all the local maxima, local minima, and saddle points of the functions f(x, y) =…

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Q: 2. If the power series defined by En=1 an (x + 1)" converges at x=3, thenE-1(-1)" an…

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Q: letfeRiemann La.bT and dE Rieman. then AFERiemann [q.b] Showthat Sraf)(x) dX Riemann in tegkal)

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Q: 4 F(s) 3s2 + 1 s - 3 1+ (8 – 3)² 1 F(s) = (s – 3)5 F(s) = s2 + 2s + 1'

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Q: Question 16 -3 25 For A = 1 0| and 6 a least-squares solution of Ax -1 4 10 What is the…

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Q: Given: 1 fett= 구 -1 Obtam the Fruries Seriesi Ans feet- Gia (2n+)t a TT 2ntl Find; ab

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Q: 2s - 1 s2 - s -- 2' F(s) = s2 – 4 - 4 F(s) : (s2 + 4)2 1 F(s) = s2 + 3s + 2

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Q: Question 4 2 1 1 1 Let V1 = V2 = 3 V3 = 1 V4 = 1 4 8 For what value of t is the set V1, V2, V3, V4}…

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Q: -2-x Q1) Evaluate the integral S* dy dx using polar coordinate 0,

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Q: QI) Evaluate the integral dy dx using polar coordinate

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Q: Q4) Find plane area inside the polar functionr = 2 and outside the polar function sin -0) +1 in…

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Q: Question 19 t Let u = it and W = Span -2 1 .For what value of t is -3 the vector U orthogonal to W?

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Q: [1 1] a Let A 2 1. Find a QR-factorization of A. If R = then the 1 3. value of a is , the value of b…

A: We can solve this using given information

Q: S(t) S(t) = t2 + 3tª. f(t) = t2 + 3t + t3/2. f(t) = t e-3t + e!.

A: The solution is given as

Q: Prove that the following limit does not exist: lim (z,9)(0,0) I-y

A: To Prove: lim(x,y)→(0,0)x+yx-y does not exists   Here, we will check the value of the limit along…

Q: Convert dzdydx /9-x-y Into an integral of cylindrical coordinates

A: To convert into polar coordinates.

Q: You are given the data points (xi, Yi) for i = 1, 2, 3 : (2, 3), (1, –8), (2, 9). If y = a + Bx is…

A: We have to apply the least squares method to solve the problem.

Q: п(x — 2)" 3" (2n – 1)3 * VI. Consider the power series - n=1 a. Show that the power series converges…

A: Given series is ∑n=1∞n(x-2)n3n(2n-1)3

Q: Question 29 Let (V, (,)) be an inner product space and let f, g be vectors in V. If ||F|| 4. ||g|| =…

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Q: Consider the linear transformation T: M22 → P2 given by a (a + 2b + c+ d) + (a + 2b + c + d)x + (a +…

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Q: Q/ Find the general Solution of the diff. equ-

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Q: Question 30 Consider the linear transformation T: M22 → P2 given by a T = (a +6 +c+ 5d) + (a + b +…

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Q: Find Duf at P. f(x, y) = 3(1 + xy) 2; P(5,3); u = 1 i+ NOTE: Enter the eract answer. Duf 62

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Q: 3. Determine whether the following series converge or diverge. 4+cos? n (3n–\n) Σ +00 (5-4(ln n)³)"…

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Q: Q5) Find volume of body bounded by z = x-y from below and z = x+y from Above inside y = x,y = 2.

A: Volume bounded by the region

Q: (a) If an 2 0 for all n E N, then an does not converge conditionally. n=1 (b) If the power series >…

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Q: Consider the linear transformation T : M22 P2 given by a T(" D= = (a + 26 + c+ d) + (a + 26 + c+ d)æ…

A: Let us considre the linear transformation T:V→W Kernel of T is obtained as Ker(T)=v∈V|T(V)=0 Range…

Q: Question 12 -9 6. The eigenvalues of 1 are 6. and

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Q: EXERCISES 2: Find all the local maxima, local minima, and saddle points of the functions f(x, y) =…

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Q: Question 21 Let V = {(x, 4) x E R}. You are given that (V,O, O) is a vector space with (1, 4) Đ (72,…

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Q: 4. Give an example of a continuous function f : (0, 1) → R that cannot be uniformly approximated by…

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Q: Convert X-6A Into an integral of spherical coordinates 4 5 SE So p?sinodpdøde 6coso psinodpdode…

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Q: For all x E R, eª = > ) n!" n=0 • Express f(x) = x²e® as a power series. • Find the third degree…

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Q: Petermine whether the following series is convergent or divergent (-1)"3n² 4n²–1 (b) n=1

A: Given series is ∑n=1∞(-1)n3n24n2-1

Q: 2. Using triple integral to find the volume of a solid whose base is the region in xy-plane (z = 0)…

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Q: Question 26 1 2 4 6 is in NulA. 3 Let A =-1 1 -1 If | 0 1 1 then the value of a is and the value of…

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Q: Let (V, (,)) be an inner product space and let v, w be vectors in V. If (v, w) = 7 and ||w|| = 5,…

A: The solution is given below. Hope this helps.

Q: Let S be the surface defined by the vector function R(u, v) = (u cos v, u – v, u sin v) with u eR…

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Q: What is the minimum number of edges for a spanning tree for this graph?

A: The given problem is related with graph theory. Given a graph. We have to find the minimum number of…

Q: H.W: Evaluate the follou

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Show clear and detailed solutions. (a) Find the general equation of the plane 2 passing through the…

A: Plane parallel to a plane ax+by+cz=d is  ax+by+cz=k