Problem #1: Solve for X1 and X2 2X1 + 4X2 = 80 3X1 + 1X2 = 60

Q: I don't understand how you got 4,-7,1

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A: yp​=−6tsin(3t)+2cos(3t)ln∣sec(3t)∣Explanation:Step 1:Step 2: Step 3: Step 4:

Q: Let 3 -4 10 -5 2 3 -7 4 A 0 0 0 0 -2 - -3 7 A basis for the null space of A is { vector

A: ​The basis for the null space of A is ⎣⎢⎢⎢⎡​2110​⎦⎥⎥⎥⎤​,⎣⎢⎢⎢⎡​1−201​⎦⎥⎥⎥⎤​ vector​Explanation:Step…

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A: We have to find the Lapace transformation

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Q: 2. Use the method of Example 3.4.3(b) to show that if 0 <c< 1, then lim (c¹/n) = 1.

A: Given, .It is required to show that, .To solve the above problem, use the following definition and…

Q: 1. Let f : (−1,1) → R, f(x) = (1+x³)-³. Compute g' : (0, 1) → R where (a) g(x) = X X f. (b) g(x) =…

A: Answers along with explanations are provided in the image. Explanation:

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Q: 4. (a) Find the area of the region under the curve f(x) (b) What the average value of f(x) : =xe-r…

A: Area under the curve is 0.80690 average value of function is 61​(e1​−e41​)Explanation:Step 1:Step…

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A: Using tree diagram we have to find the permutation of the set .

Q: wit H

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A: NOTE: As per the guidelines, repost part (d).

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A: Given that  matrix.Suppose that the QR factorization of  is  given by  .We have to find the…

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Q: parametrically define the hyperboloid 4x^2 − y^2 − z^2 = 1 .

A: Given hyperboloid We have yo parametrically define the hyperboloid.

Q: (3.2) Find the second order Taylor formula for the following functions at x0 = 1) f(x, y) = tan(2x +…

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Q: Question Two boats are sailing on a lake. The position of the first boat at time t is given…

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A: Given that a large tank is partially filled with 100 gallons of fluid in which 30 pounds of salt…

Q: 1. Write precise mathematical definition for the following terms: d) Simple graphe) Equivalence…

A: I will provide the answer, and both options are acceptable, but you can choose what's best for you,…

Q: 2 1 Suppose we want to compute e At for A = using Putzer's algorithm. The eigenvalues are 2, 3 and…

A: We have given the eigenvalues: and For the two different eigenvalues  and :

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Q: 7: Make a change of variable, : - Py, that transforms the following quadratic form into one with no…

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Q: Given the following recursively defined set S: Basis: 0 € S and 7 E S Recursive rule: if x = S and y…

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Q: 10. Let T: R2 R2 be a matrix transformation that maps u= [1] into [B] v= mape=[3] into [1] what is…

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Q: An electronics retailer sells laptops at a steady rate of 7,500 per quarter. It costs the…

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Q: 0 -1 and whose nullspace Construct a matrix whose column space contains 2 and 522 2 ] contains

A: Explanation is given below:Explanation:

Q: b 5. Does the graph bellow have a Hamiltonian path? Hamiltonian circuit? a 4 جوه a h g b с e

A: A Hamiltonian path in a graph is a path that visits every vertex exactly once. It's named after Sir…

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Q: 6. Let the reduced row echelon form of A be 1 3 04 0 5 0 0 1 3 0 2 0 0 0 1 1 0 0 0 0 0 Determine A…

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Q: Find f'(x). f(x) = 6 In (7+9x²) f'(x) = ☐

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Q: Make a change of variable, x = Py, that transforms the following quadratic form into one with no…

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Q: 1. How many more gift card raffle tickets will be entered than shopping spree raffle tickets if…

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Q: Given the sequence defined by the following recurrence relation: ⚫ b₁ = 12 . ⚫ b₁ = 29 b=5-b-1-6.…

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Q: Solve each of the initial value problems. Clearly label the general solution, and then the…

A: We have to solve the IVP