Let A 1 2 −1 -2 3 -2 -1 1 1 Diagonalize A to find A100.

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Q: Consider the HISTORICAL method you chose (Chinese Mathematics: specific Lui Hui's method to fing the…

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Q: Evaluate the expression. P(9, 2) · P(6, 5)

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Q: The graph below shows the numbers of visitors at a museum over six days. Number of visitors 330-…

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Q: 9y" + 6y' + 4y = 0; y(0) = 3, y'(0) = 4

A: (22)

Q: How many solutions are there to the equation x1+x2+x3+x4 = 17 where x1, x2, x3, x4 are integers and…

A: Number of non-negative integer solution of         x1 + x2 + ... + xn = k,  with  xi…

Q: Use row operations to solve the system.   x+ y− z= 2 4x− y+ z= −7 x− 3y+ 2z= −22       Question…

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Q: Use the Mean Value Theorem to prove: If f(x) and g(x) are differentiable on an interval (a, b) and…

A: and  are differentiable on an interval  and We have to show that  for all

Q: Find the volume V of the solid below the paraboloid z= 6 - x² - y² and above the following region.…

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Q: 3. Consider the following function f(x, y) = 1²y + 2y²-2ry +6. (a) Find all first and second order…

A: Given a two variable function such that                             We have to find : (a) All first…

Q: For each sequence, find a formula for the general term, an. Sequences start with n = 1. For example,…

A: Given, sequenceThen we write the general term of above sequence.Hence, the general term of given…

Q: Can you also help me with 10? I'm having a hard time solving it.

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Q: . How many 8 digit binary strings have exactly 5 ls?

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Q: Let K be a finite normal extension of a field F. If a, ß are any two elements of K conjugate over F,…

A: Statement : Let K be a finite normal extension of a field F. If a and b are any two elements of K…

Q: Find the general solution to the following linear system. Write the solution as the sum of the…

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Q: Find all the roots of the given function. Use preliminary analysis and graphing to find good initial…

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Q: Let K be a finite normal extension of a field F. If a, ß are any two elements of K conjugate over F,…

A: Let K be a finite normal extension of a field F. If a and b are any two elements of K conjugate over…

Q: Let A={a,b,c,d, e) and B = {d,e,f,g, h,i}. The cardinality of the set |BXAVAXB| is: A B D 30 26 4

A: Cardinality of the set.

Q: 3. Suppose that n is an odd positive integer and write o(n) a b n with gcd(a, b) = 1. Show that the…

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Q: Y(s) For the following transfer function, = F(s) where U(s) = U (s) erive the time function y(t).…

A: We have

Q: 3.8. Using the Gram- Schmidt method, turn the basis B=Cb of a two-dimensional subspace U CIR³ into…

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Q: Use Gauss Jordan method to solve x-2y+4z=20 x+y+13z=-31 -2x+6y-z=-69

A: Given system of equations:We have to solve the given system of equations by using the Gauss Jordan…

Q: 1. Give an example of a set S with a relation ~ on S such that ~ is symmetric and transitive but not…

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Q: Consider the following vectors: a= 7₁ = 1 72 = 9 2 -2 For each of the following vectors, determine…

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Q: Solve by any method 4x-4y+4z=16 -4x+4y-4z=-19 -12x+12y-12z=-49

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Q: Solve the given initial-value problem. d²x dt² + 4x = -2 sin(2t) + 3 cos(2t), x(0) = -1, x'(0) =

A: Here we can use method of separation of symbols to solve the above problem. First we find…

Q: Hence find a general solution of the equation 2 1 w" () - ¹ ()² = ² 2. w' w'

A: We have to find the general solution of the equation It is given that  and

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Q: Is the divisibility relation on Z antisymmetric?

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Q: For the vector field (x, y, z) evaluate the line integral along the curve made of three adjacent…

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Q: 4. Find the smallest positive odd integer n such that o(n) 7680 n 12121 You should do this by a…

A: We have to find the smallest positive odd integer n such that

Q: 2. NASA can create a weightless environment by flying a plane in parabolic paths. The table shows…

A: GivenTime, tHeight, h1026900152902520306002531625303210035320254031400

Q: Find the following limits. You may use any theorem we have proved, such as Arithmetic of Limits.…

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Q: Using only a simple calculator, find the values of k such that det(M) = 0, where M your answer,…

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Q: Find the values X₁ and X₂ that minimize f(x₁, x₂) = 4x₁ + 6x2 subject to the following constraints.…

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Q: Find the rank of the matrices where x, y, and z are distinct.

A: We have to find the rank of the matrix

Q: 2. In this exercise, we will construct a new finite group of order 8 using the quater- nions. The…

A: (a)  Recall  that the Quaternion group is  the group which consists   of the  eight quaternions .…

Q: Use the graph to evaluate each expression. (a) (f + g) ( − 2) (b) (f - g)(1) (c) (fg) (0) (d) (1)…

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Q: Consider the functional S[y] = [² da ln(1 + a²y'), y(1) = 0, y(2) = A, where A is a constant and y…

A: The functional  S[y] is given by an integral that depends on the function y and its derivative y′…

Q: The curves f(x)= 3-x^2 and g(x) =e^(2x)-1 are shown in the figure. Let R be the shaded region…

A: The given curves are  and .   is  the shaded region bounded by the graph and the axis.

Q: Diagonalize the following matrix. -15 -187 [-15 -15 12 15 P= D = 8 36 P-1 =

A: The given problem is to diagonalize the given matrix.Given matrix,