Let A = 3 -1 6 2 2 0 -1 6 7 7 with its entries considered as elements of the field C. Find a basis of C³ consisting of eigenvectors of A, and write down an invertible matrix P and a diagonal matrix D with DP-¹AP.

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A: A function is defined as a relation between a set of inputs  having one outputs.

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A: Solution:Given that, find the volume of the given prism:We know that, volume of the right prism

Q: F(x) = F(x) = √5 + sec (31)dt | Hint: F(x)=√5 + sec (38)dt = -- √5 + sec (31) dt) -

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Q: E (g) Find the absolute maximum and absolute minimum of g(x). 9(5)=10 On what interval(s) is g(x)…

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Q: 2. Let A = = 1 -4 -2 (a) Compute the eigenvalues of A. (b) Find a basis for each eigenspace of A.…

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Q: Problem 2. Consider the vectors and the vectors --0--0 調 and e₁ on basis of R² *-*- Use the…

A: Inner product in Euclidean space Rn: = x_1y_1+x_2y_2 +\cdots+x_ny_n \)" data-mce-style="cursor:…

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Q: How many solutions are there for the following equations and inequalities? All variables are…

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Q: 1. Consider the sets D = {: ne J}, E = DU {0}. (a) Find a continuous function f : (0,1)→ R such that…

A: Consider the sets and . (a) We seek a continuous function such that . One such function is .(b)…

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A: Given the matrix .We will find its inverse by applying the elementary row transformations.Consider…

Q: 3. Determine an inverse Laplace transform of the function. a) [¹ 10 (5-3)5 b) [¹[3e-4³ cosh(3t)]=

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Q: True/False: There exists a square real matrix A with no real eigenvalues. True O False

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Q: Hint: only one is true and the other is false

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Q: The given set is a basis for a subspace W. Use the Gram-Schmidt process to produce an orthogonal…

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Q: Suppose we are trying to show that limf(x) = L where the graph of f(x) is given below. A distance of…

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Q: 15. For what value(s) of A is the solution to the following equation positive? 9.5¹ = A answer OLA…

A: Given equation is 9⋅5−t=A   .....(1)Dividing by 9 both sides 5−t=A9 OR 5t=9A     .....(2)

Q: 3. Let F = xzi+yzj+xyk be a vector field and S be the part of the sphere x² + y² + z² = 9 that lies…

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Q: T T T F 57. For each natural number n, 4 divides (5″ − 1). F 58. For each natural number n, 2+ 4…

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A: We will use Venn Diagram to solve this problem.A Venn diagram illustrates the relationships between…

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Q: T F 64. Let f: A → B and g: B→C. Iff and g are 1-1 so is gof.

A: According to guidelines we can solve only first question, since there are multiple independent…

Q: (b) X g'(x) g'(x) Complete the table. If a value does not exist, write "DNE". 3 4 8 1

A: Given thatWe have to find the value of .

Q: 9. 10. = −2 sin (x + 1) + 1, the transformations applied are: For the function f(x): TT a)…

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Q: 2. For this system of 1st order ODE, y₁' = 4y₁ + 2y₂ −2e-²¹ Y₂' = 3y₁ +3y₂ + 3e-²¹

A: First order system

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Q: L Find the Laplace transform F(s) = {f(t)} of the function f(t) = et-2h(t-2), defined on the…

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Q: Volume of the slice, then the Mass of the slice, the Force needed to lift it, and the Work needed to…

A: Volume: Volume of this slice = πr2dhMass:Mass of this slice = Volume of slice Density of waterForce…

Q: Z= 3 15 0 - 1 3 0 - 1 - 2 V2 6 - 1 12 3

A: Assume

Q: Find the first four nonzero terms in a power series expansion about x = 0 for a general solution to…

A: The power series solution centered at x=a is given by w(x)=∑n=0∞an(x−a)n .

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Q: Find the eigenvalues of the matrix Smaller eigenvalue = Associated eigenvector = Larger eigenvalue =…

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Q: Find the optimal strategies, P and Q, for the row and column players, respectively. 28] P= X Q= X 2…

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Q: ----2 0 2 y = f(x) 4 6 8 x g(x) = f* f (t f(t)dt Find all local maximum and local minimum values of…

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Q: Let -X = x -x f(x) = Find the power series representation for the function f(x) by completing the…

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Q: 3. (a) (b) YA -2 x 0 g(x) X Let J be the function whose graph is given below. g'(x) 0 2 Complete the…

A: Note: As per our guidelines, we can solve first one as your both parts are not small. Please repost…

Q: the formula P= 14.7e^-0.21x gives the average atmospheric pressure P, in pounds per square inch, at…

A: Average atmospheric pressure

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Q: (a) J₁ J5 4 2 1 6 3 2 3 A3 7 6 5 8 A4 | 9 6 5 7 As 8 3 5 7 4 A₁ ܠ ܠ ܠ ܠ ܠ A2 125 J1 J2 J3 3 1 +3∞47…

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Q: Solve the linear differential equation using Fourier transform.

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Q: Given a subset {v₁, V2, V3} of a vector space V over the field F, where F is a field with 1+1 = 0,…

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Q: Exercise 11.2.4 Consider R3 as an inner product space with the usual dot product. For each of the…

A: Note: we will be solving part (a), (c) and (d) as asked.Consider as an inner product space with the…