1 Let F and G be two inner products on a vector space V over the real field R. If F(u, u) = G(u, u) for all u E V, show that F= G. nte in V

Q: Express in cylindrical components: (a) the vector from C(3, 2, -7) to D(-1, -4, 2); (b) a unit…

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Q: (-1)"x²n (2n)! 1. For all x € R, cos ax = n=0 (a) Find a power series that is equal to x cos(x²) for…

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Q: 17) Daniel is on a diet and he wants to limit his food intake to 109 g carbohydrate, 103 g fat, and…

A: We will form system of linear equation from given data and then solve it by matrix method to find…

Q: QUESTION 6 a) (4) Find all the distinct cosets of (4> in Z12- b) (4) List all the left cosets of H…

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Q: 7 3m converges or diverges. If it converges, find its sum. Determine whether the series m=2 Select…

A: The given series is ∑m=2∞73m.

Q: 7. Leon is a rock climbing enthusiast, and is considering getting a membership at a new rock…

A: We will find cost function for both cases and compare between them by using graph

Q: Draw a sketch of the cylinder z = -4 - y2.

A: A cartesian coordinate system contains two mutually perpendicular number lines named x-axis and…

Q: Evaluate the triple integral In(1+ Vr2 + y? +z?)dzdydr.

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Q: 5. Identify and sketch the graph of the following equations in R³. (a) x2 + 4y² + 2² – 8x + 16y – 2z…

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Q: If A = {x:x [B| None of these Option 3 O Option 4 |A| = |B| |A| < |B|

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Q: 1. Given the function f(x) = (=) %3D (a) Find a power-series representation for f(r). f(x) da = n(n…

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Q: Consider the following. -6 12 -3 -4 P = 1 A = -1 -1 -1 (a) Verify that A is diagonalizable by…

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Q: a) Show that the matrix H constructed from a matrix A, as H = i(A – A†), is Hermitian, whether A is…

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Q: Evaluate R where R is the region bounded above by the line y = 3, on the right by the circle (x -…

A: We have to evaluate ∬RydA

Q: Find parametric equations for the line whose vector equation is given. (a) (x, y) = (4, –6) + t(1,…

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Q: X1 + 5x2 + 3x3 = 30 3x1 + 7x2 + 13x3 = 80 : 2 12x1 + 3x2 – 5x3 with x", x", x"| = [1, 2, 3] until…

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Q: Upload your solutions here for the following problems on Determinants. 1) 3 6. 1 -2 3 1 4 A = 1 -1 1…

A: To find the determinant

Q: Find a formula in terms of k for the entries of Ak, where A is the diagonalizable matrix below. 17…

A: The solution is given as

Q: Is it true that Arg(z) = arctan for x + 0, where x = Re(z) and y = Im (z) ?

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Q: Q2/ Solve the following systems of linear equations. Use Gausssian elimination and give the solution…

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Q: Identify and sketch the graph of the following equations in R³ (a) x2 + 4y² + z² – 8x + 16y – 2z +…

A: we can add or subtract same amount from a equation to simplify equation. The logarithm function…

Q: 4. Show that =N} which is subset of R is not compact by describing an open cover for n it that has…

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Q: Use a software program or a graphing utility with matrix capabilities to write v as a linear…

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Q: Is it true that the quotient of two complex number is obtained by dividing their moduli and…

A: Given question says "Is it true that the quotient of two complex number is obtained by dividing…

Q: Show that y = x is a solution of the differential equation x^2 y” – (2x + x^2 )y’ + (2 + x)y = 0,…

A: The solution is given as

Q: You have 7,264 grams of a radioactive kind of neptunium. How much neptunium will be left after 80…

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Q: 11. Convert the cylindrical coordinates (4,,-2) to rectangular coordinates

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Q: Part III: Use the graph of f(x) to sketch y = f(x) 5 4 하 2 6 -5 -4 -3 -2 123456 -3 4 -하 -6

A: Given: y=f(x) To draw: y=0.5f(x)

Q: What two months would the price land on the slanted midline?

A: Here is the actual graph of the price and the midline.

Q: Use Lagrange multipliers to find a vector in 3-space whose length is 6/3 and whose components have…

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Q: (-1)"x2" (2n)! +0o Σ For all x E R, cos x = n=0 a. Find a power series that is equal to x cos(x²)…

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Q: Consider the following function: -- 2, -2 < r <-1 f(x) = {1, 2-z, 1<r$ 2. (1) Sketch the graph of f…

A: Given the function fx=-x-2, -2≤x≤-1x,           -1≤x≤12-x,         1&lt;x≤2. Sketching its graph,…

Q: Use the given transformation to evaluate the integral. | 5x2 dA, where R is the region bounded by…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Use a graphing utility with matrix capabilities to find the following, where u = (2, 1, 1, –3), v =…

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Q: x R y in R if | x |=||

A: we have to find the relation R where R is defined by x R y in ℝ if x=y, equivalent or not.

Q: A fire truck is to be added to a certain district.  Which district should get the fire truck?…

A: Given: Number of Trucks in district 1=18 Number of houses in district 1=23208 Number of trucks in…

Q: dy Find the solution to the differential equation da 6xy (In y)² which passes through the point…

A: Given differential equation is dydx = 6xy(ln y)2

Q: The functions: ƒj(x) = 7x and f2(x) = 2x form %3D a fundamental set of solutions of the DE: x²y" –…

A: (1) Given the function f1x=7x &amp; f2x=2x2 we have to show that these function form a fundamental…

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: To find the distance from point P to the line AB .

Q: 1. For all x E R, cos x = ) (2n)! n=0 a. Find a power series that is equal to x cos(x²) for all x E…

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Q: Determine if the two vectors are parallel, orthogonal, or neither. Show your proof a) A = and B =…

A: We have to determine that the given vectors are parallel , orthogonal , or neither.          (a) A→…

Q: PROBLEM 30. For (x, y) and (u, v) in R2, define (x, y) ~ (u, v) if x² + y² = u? + v?. Prove that…

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Q: Find the three cube roots of -8i. Express your answers in polar form and the convert them into…

A: To find the cube root of -8i Let z = -8i

Q: Explain why S is not a basis for R. S = {(6, 1, 4), (8, 6, 13), (3, 1, –5), (0, 3, 6)} O sis…

A: Solution

Q: Does the function F(x) = -x have a cycle of prime period 2? %3D

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Q: Consider the Taylor polynomial T,(x) centered at x = 20 for all n for the function f(x) = , where i…

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Q: 1. Solve the heat conduction equation with the prescribed initial and boundary conditions: Uxx = Ut…

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Q: Find the solutions of the equation z6 - 1 = 0. Plot the answers on an Argand diagram

A: We have to solve the equation z6 -1 =0.

Q: If y' = х-у then its solution is x+y'

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Q: A = [3 +m ,B = [m land C = [" 10" lFind the matrix X, if -2 14 – m 6 1. Let 8 + m -21 Find the…

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