Problem 3. (a) (b) (c) Let A be an n x n matrix with characteristic polynomial: +an-2 +...+ a₁t+ao f(t) = (-1)" " + an-1t"-1 Which terms of f(t) represent det(4)? If A is invertible, prove that A¹ = (-1/a₂)[(-1)" 4"-¹ +an-1-4-²+A₁-2t¹-¹ +...+₁₂] 12 1 3 Calculate A¹ for A = 0 2 00-1 by using (b).

Q: Evaluate the work done between point 1 and point 2 for the conservative field F. Here you can assume…

A: Given: F=5xi+5yj+5zk; P14, 1, 4, P27, 5, 9 The Vector field is conservative. To find the work done.

Q: If a₁, 92, a, are in arithmetic progression, where a > 0 for all i, then show that 1 √a₁ + √a₂ 11 +…

A:

Q: Find the surface area generated by rotating the given curve about the y-axis. x = ett, y = 4et/2, y…

A:

Q: Solve ty' - y = t²e-t assuming t > 0.

A:

Q: Let C be a constant such that the integral converges. Find C and evaluate the integral. C = 6 14 x+1…

A:

Q: a. How large is the property in​ acres? b. If the property is selling for $450,000​, what is the…

A: Given , Area of property = 15 hectares   Also 1 acre = 0.4 hectare   Price per acre = $450,000  We…

Q: Find 100 ΣΩ (2k – 20) k=6

A:

Q: CONSIDER A FUNCTION F: [-3,3] => R WHOSE SIGNALS VALUES AND THE DERIVATIVES ARE SHOWN BELOW. FIND…

A: Consider a function F : -3, 3 →ℝ, Given table is Intervals f f' f'' x<-2 - - +…

Q: If s, is the arc length of locus of centre of curvature, then show that 2 √√k²q² +k¹². k² (² e ds₁…

A:

Q: (a) How many nonnegative integer solutions are there to the equation ₁ + x₂ + x3 + x₁ = a? (b) How…

A:

Q: 19) If f/u) = sinul; then (fog)(3) = ? A) O B) 1 M= g(x)=x²-9₂ c) 6 D) 9 E) None

A:

Q: Which of the following statements are correct? (Select all that apply.) 0 0 0 0 xa xª 1 xo xª-b □…

A: We now solve the given problem by explaining each options separately.

Q: A thin bar of length L = 3 meters is situated along the x axis so that one end is at x = 0 and the…

A: Given: Function, f(x)=150-15x           Boundary conditions: u0,t=u3,t=0To find: ux,t, u42, 0.1

Q: The Palermo scale value of any object can be found using the equation PS= log₁0 R, where R is the…

A:

Q: Determine the solution of the following differential equations. a) (D² +9) y = 81x² + 14cos3x

A: Solution of the non- homogeneous differential equations

Q: 1. Find the value of k so that the ODE (y³ + kxy¹ − 2x) dx + (3xy² + 20x²y³)dy = 0..

A:

Q: Please help me answer 4Di, and 9

A:

Q: Ⓒ find the vertices and asymtotes for the hyperbola defined by the (x²/16)-(²/25) = 1 following…

A:

Q: Question 6 Using Green's Theorem, compute the counterclockwise circulation of F around the closed…

A:

Q: Use the Linearization Theorem to classify the equilibrium point y = 0

A: To Linearization  dydt=ycos(4πey) and classify the equilibrium point y = 0.

Q: Find the Laplace transform of 1.- L(2x + 3x³ - 5x² + 7x - 1) Value of 3.33%

A:

Q: For the right triangle below, find the length of x.. 15 A) Express answer as a simplifed radical. T1…

A:

Q: Let L₁ be the line parametrized by (4-2t, 2-t, 3+t). Let L₂ be the line parallel to L₁ going through…

A:

Q: 2 Use the method of Lagrange multipliers to find the point that, realizes the minimum value of the…

A:

Q: Working directly from the definition (not using Arithmetic of Limits or any other results proved in…

A: Given fx=x2 To prove: limx→3  x2 =9.

Q: [ 2xy²zda + 2a²yzdy + (x²y² − 2z)dz where C' is the curve given sint, 0≤ t ≤ 27 traversed in the…

A:

Q: Let F = . Use Stokes' Theorem to evaluate If cu S curlF.ds, where 2 S is the part of the paraboloid…

A: Given That : The vector field F→=-yzi^+xzj^+xyk^ S is the part of the paraboloid z=13-x2-y2 that…

Q: Cn Let A = a₁ + a₂ + ... +an, B₂=b₁ + b₂ + b3 + ... + b₂ D₂ = C₁ +C₂2+...+c, and cn=a₁bn +…

A:

Q: Solve this linear programming problem using graphical methods. Restrict  x ≥ 0  and  y ≥ 0. Maximize…

A:

Q: Solve the following system of differential equations (x' = 2x + y ly' = x + 2y 1. y'

A:

Q: Calculate Ji F. ds where S F = (4x³z, 4y³z, 3z4) and S is the surface of the solid bounded by the…

A:

Q: a. Find all the intersection points of the following curves. b. Find the area of the entire region…

A: The given problem is to find the intersection points between the given polar curves and also to find…

Q: Problem IV Let V be a subspace of Rª spanned by three vectors given below. Find the distance from…

A:

Q: Let p be a prime number. Prove that for any natural number n we have   | GL (n, Zp ) | = (pn -…

A: To Prove:  GLn,ℤp=pn-1pn-ppn-p2....pn-pn-1, where p is a prime.

Q: Diagonalize the matrix A, if possible. That is, find an invertible matrix P and a diagonal matrix D…

A:

Q: 3. Pick an interesting positive integer a with a > 20. 1 (a) How many nonnegative integer solutions…

A: It is given that a>20. (a) The objective is to determine the number of nonnegative integer…

Q: 83. PR bisects ZQPS & PRIOS P APQR = A by R S ΠΟ

A: Given , PR bisects <QPS and PR is perpendicular to QS , we need to find whether ∆PQR to congruent…

Q: Problem separate figures for each. (Each is a subset of R2.) ). Sketch each of the following…

A: To sketch the Cartesian product

Q: em 8.5. Let a 2 100. We have (x) > log loga.

A:

Q: 4. Solve dy d.x. 3y² - x² XU . Note: your solution may be left in implicit form.

A: Use variable separation method after y substitution to solve.

Q: ries converges or diverg verify that the condit n² +3 Σ(1²2+3³3 2n² + 1 n=1 72

A:

Q: Verify Stokes' Theorem for the given vector field and surface, oriented with an upward-pointing…

A: Solving the above question of stokes theorem

Q: ILLUSTRATION 4.58 Find the equation of the plane which contains the line of intersection of the…

A:

Q: Topic: Maxima-minima/optimization problems: Algebraic Functions A carpenter wants to make a…

A:

Q: Use sets  U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10},   A = {2, 4, 5, 7},  and  B = {1, 3, 4, 5, 6, 9, 10}…

A:

Q: Find C1 and C₂ so that y = c₁eª +c₂e¯ª is a solution of the IVP y"−y=0,_y(1)= 0, y′(1) = e

A:

Q: Use the Divergence Theorem to calculate the flux of the vector fields F₁ = −4zi + 4xk and F₂ = −4zi…

A: Given That : Vector Fields are F1→=-4zi^+4xk^ and F2→=-4zi^+1-4yj^+4xk^  To Find : Using the…

Q: Let á 9 = [-₁0] and 6 = [₁₁] 10 Compute the projection of a onto band the vector component of a…

A:

Q: Let the n x n matrix A be given in the Reference Page. Find the determinant of the matrix when n =…

A:

Q: 5. Let h - Ah = x = [1 + ²√5 h = √5], 0 where h is a real parameter. (a) Find all values of h for…

A: The question is from stability analysis.