Let A = 4 -1 and v= 1 -1 4 Then orthogonally diagonalize A. 1 1 Verify that 5 is an eigenvalue of A and v is an eigenvector.

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A: Given the relative error in computing the volume is 2.39%

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Q: The first term of a G. P. is 1. The sum of the third and fifth terms is 90.

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Q: Problem 1: Find the linear combination 2a +33 + 4y = b. Then write b as a matrix-vector…

A: Given that        α=111, β=011,  γ=001 We need to find the given linear combination.

Q: a) [The set v = U2 U1- - V2. [2].110 b) a basis for R². The set S = If v E span{v₁, U₂}, then U = ◆…

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Q: A coin is tossed three times, where (i) A: head on third toss, B: heads on first two tosses (ii) A:…

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Q: Obtain the general solution. (HOMOGENOUS EQUATION) 3. ydx + (2x - y)dy = 0

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Q: Diagonalize the quadratic form by finding an orthogonal matrix Q such that the change of variable…

A: Given Quadratic form is  Q=6x12 +9x22 -4x1x2                            ⇒…

Q: 4. Solve the recurrence relation an = 5an-1-6an-2 (n> 1) subject to the initial conditions ao = 1,…

A: Given recurrence relation an=5an-1-6an-2 subject to  a0=1a1=1

Q: 2. f(x) = x + 1 4 e --2 2 0 +2 4. f(x) = (x-3)5 4 1-2 ty +2 ^y 0 --2 6. f(x) = (x+2)³ - 2 -2-- A 0 2…

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Q: ILLUSTRATION 5.40 If (p+q)th term of a G.P. is 'a' and its (p - q)th term is 'b' where a, b>0, then…

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Q: Does there exist a geometric progression containing 27, 8 and 12 as three of its terms? If it…

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Q: 4. a) Find the surface area of the part of the sphere x² + y² + z² = 4 that lies above the plane z =…

A: note : Since you have posted multiple questions, we will provide the solution only to the first…

Q: (5) Let f(x) = 5x² + for x > 0, where A is a positive constant. Find the smallest A such that f(x) ≥…

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Q: Consider the integral I = fa x arctan(x) dx. (a) Write explicitly an approximation for I using the…

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Q: Problem 2: Let A 11 [ -2 0 0 -1 - 1 002 2 (1) Find the eigenvalues and eigenvectors of A; (2) Find…

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Q: Prove that y R³ as a linear combination of (5) Is a basis of R³ {0·0·0)}

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Q: Let Z₁, Z2, Z3 be the complex numbers such that Z3 - Z1 |Z₁-1|=|2₂-1| = |z3 − 1| and arg Z2 - Z1…

A: As there is no z1 in the expression whose value we have to find out, first we will assign a value to…

Q: A truncated octahedron is a polyhedron with 14 faces, of which 6 are squares and 8 hexagons. How…

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Q: 3. If f, g and h are functions so that the composition makes sense, then the composition of the…

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Q: Find a function that satisfies the given conditions and sketch its graph. lim f(x)=0, lim f(x) = ∞o,…

A: limx→±∞fx=0, limx→5-fx=∞, limx→5+fx=∞,  Lets check each of the given options.

Q: Which of the following is an element of the set of vectors in R³ of the a form Select one: O None of…

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Q: Consider the function f(x) = x² +9 X - 2 A) Find the intervals of increase or decrease of f(x). B)…

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Q: Please write this out on paper, I cannot really understand this typed format!

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Q: Exercise 2.20 Find the Fenchel conjugate for each of the following functions on R: (i) f(x) = ex. {…

A: note : Since you have posted multiple questions with multiple sub parts, we will provide the…

Q: VUChoose the value for a such that OWN7 O KV-7 O O O TL None of the others 7 TL f'f#4x²ycos(ax) dx…

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Q: Give an algorithm (write the pseudocode) that takes in a list of n integers and returns the location…

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Q: numbers The summ e of i'm finite of terms in Gy.p. is 20, and the sum of their squars is loo, the…

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Q: 5. The series is n=0 (sin 2) 3n 10n (a) A convergent p series. (b) A divergent p series. (c) A…

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Q: or each of the following series, determine whether the series converges or diverges. (Sum from 1 to…

A: p-series Test : A series of the form ∑n=1∞1np is called p-series, its convergent when 0&lt;p&lt;1…

Q: Q5: Find and ax fat (x,y)=(1,0) if f(u, v₁w) = u² + v² + w²₁u = xy, v = xcosy and w = xsiny. (

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Q: D. Determine whether each of the following series are absolutely convergent, conditionally…

A: We have the following infinite sums : ∑ (-2)n2 / (n + 2)! ∑ (-3)n / (3n2 + 6n) ∑ (-4)n / ( 4n⋅√2n…

Q: If a sample proportion is 0.64, which of the following could be a 90% confidence interval for the…

A: Given that If a sample proportion is 0.64.

Q: Let x(t) = x' (t) x' (t) = If x (0) = x₂ (t) = x₁ (t) x₂ (t) be a solution to the system of…

A: x'1t=-10x1t-3x2tx'2t=14x1t+3x2tx0=5-3∴x10=5    x20=-3

Q: (A) Suppose R is the region in the fourth quadrant bounded by the circle x² + y² = 9, 0. Sketch the…

A: Sketch the region then use the appropriate limits to evaluate integral.

Q: If the A.M. and G.M. between two numbers are in the ratio mn, then prove that the numbers are in the…

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Q: Given: A = [1 3 3 202 € M3 33 (a) Find the eigenvalues of A and determine their algebraic…

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Q: Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F and…

A: F→=9x3y2i^+92x4yj^

Q: Q1: Find the equation of the pi ne containing the points A(0,0,0), B(2,0,-1) and C(2,-1,0) then find…

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Q: Find the equation of the pi containing the points A(0,0,0), B(2,0,-1) and C(2,-1,0) then find the…

A: We have to find the plane of equation using given points.

Q: Let λ ER and consider the matrix J = 1 0 X 0 0 00 1 0 0 λ 1 0 0 X € M4. (a) Show that A is the only…

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Q: D. Determine whether each of the following series are absolutely convergent, conditionally…

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Q: Let W be the set of all vectors I y z+y with x and y real. Find a basis of W

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Q: 2. a. Find the value of 21-dx x b. Use the trapezoidal rule with four trapezoids to find an…

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Q: Evaluate ∞ ſte²¹ sin 6t dt. [Hint: Use the definition of Laplace transform]

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Q: Let G = S4 and N {e, (1, 2) (3, 4), (1, 3) (2, 4), (1, 4) (2,3)}. Show that N is a normal subgroup.…

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Q: Find two linearly independent vectors perpendicular to the vector v = نا دیا دیا -3

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Q: Determine whether the following equality is true or false. 3 ff f(x,y)dA = [³ f√√¹8-x²ƒ(x,y) dydx D…

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