40. A particle traveling in a straight line is located at the point (1,−1, 2) and has speed 2 at time t = 0. The particle moves to- ward the point (3, 0, 3) with constant acceleration 2i + j + k. Find its position vector r(t) at time t.

Q: [₂(t)] is(t) 圓 (t) dis(t) (t) [a(t)] 12(t) g(t)=[1 1 0 0] xa(t) [ra(t)] 9. Given the output…

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Q: 3. Is H closed under scalar multiplication? If it is, enter CLOSED. If it is not, enter a scalar in…

A: 3. Correct format for red box is    2,[[1,0],[0,1]]   Explanation  for this ans is in the next step.

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A: The solution is given as

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A: Please see the attachment

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Q: 4 Let A b [² }] Find Conditions on 1 c d a,b,c and d that AX =0 that AX=0 has infinitely many…

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Q: RES. Find the area of each irregular figures. Write your answer INSIDE THE AG 6 cm 4 cm 6 cm ft 8 cm…

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A: For the solution of the problem follow the next step.

Q: Find singular value decompositions (SVDs) of the matrices A [101] 1 and B= [10 10 84.

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A: we have  d=1.4θ implies, θ=d1.4

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Q: Verify the final value theorem of f(t) = e¯t(t + 2)². 2 0 4 6 = Find the initial value of the…

A: Intial and final value of the transformation

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A: For the detailed solution of the problem follow the next step.

Q: Let R1 and R2 be the relations represented in the matrix. 111 1 100 1 0 1 1 1 11 0 0 0 1 1 0 1 0 R1…

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Q: Solve the initial value problem using a power series. y" + 1xy' - 4y = 0, y(0) = 9, y'(0) = 0.…

A: Please see the attachments

Q: Instruction: Answer the following: I. Prove: S L{cos at} = 2+²

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Q: Consider z as function of the variables x and y, it is defined by : z = ln(x7y⁹) + a and P(-1, 1) a…

A: Gradient of a scalar point function z=fx,y ∇z=∂∂xi^+∂∂yj^fx,y Directional derivative of the function…

Q: (a) Show that V(x, y) = ln(1 + ²) + y² is a Lyapunov function for the system x' (t)= x(y-1), y(t)=-…

A: As per your query the solution of the part (a) of the problem 4 has been given in the next step.

Q: 7) Determine which values of K, will give 1, no solution, infinitely a unique Solution. 2 many…

A: To determine the values of k will give a unique solution, no solution, infinitely many solutions.

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A: Solution:

Q: 2. (37.4) Use the Maclaurin series for e, cos x, and sinx to prove Euler's formula eie cos 0 + i sin…

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Q: Exercise 3. Show that Equation (22) is indeed a solution of Equation (20). Verify that, taking po 1,…

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Q: Let R1 and R2 be the relations represented in the matrix. 1001 11 1 1 1 1 1 11 0 1 0 0 0 1 1 0 1 0…

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Q: Let a and b be positive integers with (a, b) = 1. Show that if g is a primitive root (mod ab), then…

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Q: Consider the inhomogeneous DE 12 + 6 + 5y = 26 sin(t) dt² dt e. Use the complex number approach to…

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A: This is a problem of parametric form.

Q: 10. 1 -1 f(t) 3 1

A: Laplace transform of the function

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A: Solution

Q: Approximate the following integrals using the following methods. ²1²1² (₁-x²-x²) -x² - y²)dydx

A: Solution :-

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Q: 2: 2x²y + 4xy + 3y = 0

A: Solution :- As per guidelines.

Q: 23 Find a 4 by 4 permutation matrix (call it A) that needs 3 row exchanges to reach the end of…

A: Take A=0001100001000010. Since, the following three row exchanges are required to reach the end of…

Q: :-Solve the following equations (choose tow only):- 1: x²y=- 2xy + 2y = 2x³ ex

A: Solution of the cauchy Euler's differential equation

Q: . Find the laplace transform of the 1VP: y" - 4y = et + t, y = y'(0) = y" (0) = 0

A: Since you have posted multiple questions and we can answer one question. So, answered the first…

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Q: divisible by 3 for

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Q: Given a basis B = {(1, -2, 2), (2, 2, 1), (2, -1, -2)) for R³, - Use the Gram-Schmidt…

A: As you ask multiple different questions so I have to solve only the first one , but for you I solve…

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A: The given problem is related with linear algebra. Given the symmetric matrix,…

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