, counting the multiplicities. Then A is orthogonally diagonalizable.

Q: F. Directions: Give the converse, inverse, and contrapositive of the following propositions. 26. If…

A: To find converse, inverse, and contrapositive of given statements

Q: Question 7 4 1 1 1 1 4 1 1 You are given that the eigenvalues of A = 1 are 1 4 1 1 1 1 4 7,3, 3, 3,…

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Q: Let (V, (,)) be an inner product space and let f,g be vectors in V. If || F|| = 4. ||g|| = 5 and ||…

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

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Q: (x -2) Given : an? + 4 (1.) Show that the reries converges conditionally when x - 1 ( 2.) Find the…

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Q: Let [7 -37 A = -4 -1 -6 -2 7 -7 a Define the linear transformation T : R³ → R³ by T(ã) = Aã. Find…

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Q: Let H = Span{1 + x²,1+x, 2 + + a", 3+ 2x + x?}. dim H? What is

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Q: (-1)" Given: sin x x2n+1 for x E R 2 (2n + 1)! n=0 (-1)"(2n + 1) 4" (2n + 1)! Compute the exact…

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Q: Use double integral polar coordinates to find the area of the portion of the surface 3z = xy that…

A: Surface are of the surface z=fx,y is given by S=∫∫A 1+zx2+zy2 dA where A is the projection of the…

Q: 1 List the elements of each of the (a) The set of integers between 1 and 50 that are divisible by e…

A: We have to right the givens sets into roaster from of set notation.

Q: (-1)" Consider the series expansion of the cosine function cos(x) = )) -x2n for all x € R. (2n)! n=0…

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Q: IV. Determine if the given is convergent or divergent. n Σ #2. L in? + 1)² n=1 %23

A: To find Whether the series converges or diverges.

Q: Sheet 3 Numerical analysis QI/ Use the polynomial that fits data shown by Newton divided difference…

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

Q: [1] Construct a 2 × 2 symmetric matrix A such that A 3 and -2] -2 8 a11 012 If A = a21 then the…

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Q: Given do -[ and d = . Then do and d, are G- conjugate if G is Non of these O D B O A

A: We want to find matrix G for which vectors are G - conjugate

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

A: Eigen values of the Matrix are

Q: The location of a point on the Cartesian coordinate system (x,y,z) is (4,5,6). Using the location in…

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Q: 2\2 1 .5, p=1 Vp² Is the series divergent or convergent? + 8

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

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Q: U& Newtans Method with XI=1 to find the root of theequation x²-X=4(rand tò Siy.deamaH Solve the…

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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: 1. The area B is given by { x² (x, y, z) E R² y? < 1, 2 = x² – y? B = 9 Assign Stokes' integral…

A: Given : area B is given by      B=x, y, z∈ℝ3 | x24+y29≤1, z=x2-y2 Assign Stokes' integral theorem…

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: Find whether the shown expression below diverges or converges Show your solution and how you came up…

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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 the region

Q: Evaluate the Inverse Laplace Transform F(s)= s+ 3s + 2

A: Problem is solved using concept of inverse laplase.

Q: Given the series, is it convergent or divergent? Eto 4+cos?n n%=1 3n-Vn n%=D1

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Q: Evaluate the Inverse Laplace Transform F(S)=T51)² -2

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Q: 2. — 4х, + 2х, — — 6 4x1 2x2 Зх, — 5х, 1

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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: 1 3 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: Qz/Evaluate the complex integral: e? dz (z+ 1)(z – 2) where C is: a) The circle Iz| = 3 b) The…

A: 2 Given integral is ∮Cezz+1z−2dz. a We have to evaluate the given integral if Cis the circle z=3.…

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: 10 You have carried out an experiment to investigate the effect of the length of a pendulum on the…

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Q: Question 8 Let B = {b1, b2} be a basis for a vector space V. Let T : V > V be a linear…

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Q: too Consider the power series > 22n (2.r- 1)". Vn? +1 n=1 3. Determine the radius and interval of…

A: A series will be  conditionally convergent if and only if the series  is convergent, but the series…

Q: Consider the following initial value problem, in which an input of large amplitude and short…

A: Inverse Laplace transferom

Q: Q3) Evaluate triple integral f " dz dx dy. ェーy

A: Given Triple integral is ∫02∫0y∫x-yx+ydzdxdy

Q: Let B = {b1, b2} and C = {c1, c2} be two bases for R?, where 31 b1 b2 C2 7 3 10 22 b] what is the…

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Q: 3. 37 Consider the orthogonal basis B = -3 10 of R3. 3 1 5 Let v = -64 15 a If vB =|b|, what is the…

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Q: Ans feer- Given: ftt 1 -1 Obtam the Fruries Seriesi Ans: fee= TT 2nt1 Find; ab

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

Q: Refer to the System of Linear Equations below. 4x1- X2- X3 = 3 -2x +6x2 +x3=9 X1 +X2 +7xg = -6 Using…

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Q: In x2/25+ x2 dx , we let x = 5sine. A True B) False

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Q: 2) Solve the D.E xdy + (2y-x+3x)dx 0

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Q: Question 10 Consider the linear transformation T : P2 → M22 given by [4a + c T(a + bx + ca2) : You…

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Q: Σ -1)2n Find a power series representation for (2n)! It is known that for all x ER, cos x = n=0 +00…

A: This is a problem of Taylor series.

Q: Suppose that T is a linear transformation such that * (H) -, -(H)-[- T T Write T as a matrix…

A: Solution

Q: 4) Find plane area inside the polar function r = 2 and outside the polar function r = sin -0) +1 in…

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Q: Convert dzdydx Into an integral of spherical coordinates (6coso p²sinodpdøde psinødpdøde Option 1…

A: We can solve this using spherical coordinates x = p sin(phi) cos(θ) y = p sin(phi) sin(θ) z= pcosϕ