1. Let A = (ai)nxn be symmetric and positive definite. Show that a) a>0, i=1,2,...,n. b) |a|<(a¡a„)³, i, j=1,2,...,n.

Q: b. Use the Gaussian Elimination method to solve the system of linear equations as follow. 2x1 X1…

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Q: 4 1-2 sin 0 equation of the conic (b) Given r = - Find the distances from the pole to the vertices…

A: Given- Given r = 41 - 2sinθ.  To find- Find the distances from the pole to the vertices and then…

Q: Try this: Solve the following DE. 1. (x-3y + 2)dx + 3(x+3y-4)dy = 0 2. (2x+3y-5)dx + (3x-y-2)dy = 0…

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Q: 1 ? < 40. The cubic x³ - 2x² - x + 1 has three real roots; one is negative. a. Find a rearrangement…

A: Solution :-

Q: Solve (x ^ 2 * y ^ 2 + 5xy + 2) * ydx + (x ^ 2 * y ^ 2 + 4xy + 2) * xdy = 0

A: As we have x(x2y2+4xy+2)dy+y(x2y2+5xy+2)dx=0∴x3y2+4x2y+2xdy=-x2y3-5xy2-2ydx

Q: 10- Find a and b in y-a.cos bx using the nonlinear least square method to fit the following data (bx…

A: Given that: x 0.1 0.3 0.5 0.7 0.9 y 0.68689 0.60040 0.43513 0.21407 -0.03443 The objective…

Q: 2.1 Given that: f = (i Cos 8 + j Sin 0 ) is a unit vector in the direction of f and that 6 = (- i…

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Q: Find a basis for the subspace of R3 spanned by S. S = {(1, 3, 6), (-1, 4, 6), (2, 4, 1)} EEE

A: Basis of subspace of ℝ3 i) It must be linearly independent. ii) Its span ℝ3

Q: Four-legged animals run with two different types of motion: trotting and galloping. An animal that…

A: To fit an exponential curve y=axb, take natural logarithm on both sides of the equation and convert…

Q: Refer to the table of the six basic solutions to the e-system. The following chart depicts basic…

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Q: Group II) Prove that: ()) =Σ(") ((-3)*(

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Q: 8. Find the singular value decomposition of the matrix below.Use Sage to find the eigenvalues and…

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Q: Use the method for solving homogeneous equations to solve the following differential equation. dx_…

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Q: Hey please reply as soon as posible If it is known that the function y1(x) = x2 is a solution of…

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Q: Given the following matrices A and B, find an invertible matrix U such that UA = B: You can resize a…

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Q: Translate into English: a. ∀x(E(x) ⇾ E(x + 2)). b. ∀x∃y(sin(x) =y). c. ∀y∃x(sin(x) = y). d. ∀x∀y(x3…

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Q: 14. Evaluate this cubic polynomial for x = 1.32, using both rounding and chopping to three digits at…

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Q: Let f be a function such that Vf(x, y) = (2x, 1) g(x, y) = x² + y². Find all the points on the curve…

A: Let f be a function such that ∇f(x, y)=2x, 1 and let g(x, y)=x2+y2 We have to find all the points on…

Q: the point (-2, 0). Find the minimum rate of change of f(x, y) = x²e-2y at

A: Given: A function f(x, y)=x2e-2y and a point (-2, 0). To find: The minimum rate of change of a given…

Q: a. Solve by back-substitution: 3x1 + 3x2 + x3 = 12, -4x₂-3x3 = -10, 2x3 = 4. b. Solve by…

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Q: 2. Give an example of a bounded variation function f: [0,1] → R. Verify your answer (i.e., prove…

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Q: The system cannot be solved by matrix inverse methods. Find a method that could be used and then…

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Q: Xx: the function f(x) = 2 * sincx) - e/4-1 is Zero for two values near x = -5. use bisection to find…

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Q: Let (Un) be a sequence of open sets in R then a) U₁is open, b) nis open.

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Q: end of its life. Operating anc the city's MARR is 7% per ye

A: Given: Life of sewage system is 40 years. Interest rate is 0.8

Q: -Find the intercepts, the symmetry for the polar equation r = cos20 anc draw it.

A: A polar coordinate is represented as r, θ, where the length such that r=x2+y2 and θ is the angle…

Q: One of the two tables below shows data that can best be modeled by a linear function, and the other…

A: To identify the given functions maybe just need to compare the values using general form of linear…

Q: Which of the following statements is correct O A. An elementary n x n matrix has either n or n +1…

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Q: 1) let (X, T) be a topological space and A, BEX. In this case, show the following a) = 0 а) бала " a…

A: Given that X, τ is a topological space and A, B⊂X . To show: (a) if A is open , then ∂A∩A =ϕ…

Q: Find the volume of the given solid over the indicated region of integration. f(x,y)=2x+2y+7;…

A: We find required volume of given region.

Q: with the given function, please identify and sketch its domain. 2 f(x, y) = ln ( 4 - x² - y²) - JJ…

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Q: Altitude (m) Temperature (°F) Plane Altitude and Outside Temperature 0 500 1000 1500 2000 2500 3000…

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Q: (x³ - 6) dx x4 24x + 3 Select the correct response: 1 — ln(x¹ — 24x + 3) + c - ○ 4ln(x¹ − 24x + 3) +…

A: ∫x3-6dxx4-24x+3

Q: Find the general solution of the system whose augmented matrix is given below. 1 -1 2 -1 -17 0 5 5…

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Q: Find a basis for the subspace of R* spanned by S. S = {(64, -21, 9, 27), (-21, 7, -3, -9), (6, -2,…

A: B is called the basis for the subspace of ℝ4 spanned by S  if i) B is linearly independent  ii) B…

Q: (b) Solve the initial value problem y" - 3y + 2y = 0, y(0) = -3, y'(0) = 5 by Laplace transforms.

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Q: y!!(t) — 10y(t) + 9y¹(t) — 90y sec(3t) =

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Q: Assignment Questions: 1. Let S={(1, 0, -1, -1),(1, -1, 1, 2), (5, 2, -9, -11)} CR¹. a) Show that S…

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Q: ank is 10 meters above the street l o that the truck can pass under the

A: Given, Span= 24 meters, Height= 16 meters.

Q: 2. Finite subsets of Rd are closed.

A: Here we have to prove that any finite subset of ℝd is closed. Here we can use that union of close…

Q: According to data collected during one year in a large metropolitan community, 30% of commuters used…

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Q: A tank of capacity 300 liters originally contains 80 litres of brine with 1/8 kg of salt. A mixture…

A: Please check the inflow rate oland outflow rate, given that outflow rate is more than the inflow…

Q: Find the domain and range of the function: g(x, y) = √16-4x² - y²

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Q: use the definition of L{} to determine {te¹t}.

A: To determine L{te4t}

Q: (a) Consider the differential equation dy dr (i) Solve the equation. (ii) Does the IVP consisting of…

A: Since you have posted a multiple question according to guildlines I will solve first(Qa)   question…

Q: let x be a discrete topology Find ent (A) blit int (A) jet AC X and

A: Given that A⊂X where X is a discrete topology. To find: (i) ext (A).             (ii) b(A).…

Q: During their freshman year, Derek's GPA was 3.5 and Terry's was 3.1. During their sophomore year,…

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Q: Find the Laplace transform Y(s) = L{y} of the solution of the given initial value problem. y" +9y =…

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Q: Convert the following binary numbers to hexadecimal: 33. 1111 10012 34. 1010 00112 35. 0001 11112…

A: Sol: (33) 1111  10012 = F916Starting from the least significant bit, we partition the binary number…

Q: Question: ym(t) — 10yn(t) + 9y/(t) — 90y sec(3t)

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