### Finding the Eigenvalue Expansion

Find the eigenvalue solution of: y^ IV = 0 y (0) = y' (0) = y (a) = y'(a) = 0

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Find the eigenvalue solution of: y^ IV = 0 y (0) = y' (0) = y (a) = y'(a) = 0

1. Solve the Initial Value Problem x' = 3 x^2/3 , x(0) = 0. 2. Show that if we change the IVP to x(0) = 1, the same system , that is x' = 3 x^2/3, still has a unique solution on the interval ( minus infinity, plus infinity).

Question 1: Solve these linear equations for x, y, and z, 3x + 5y - 2x = 20 4x - 10y - z = -25 x + y - z = 5 the value of x is in the range (1) -4 <= x <= -3 (2) -2 <= x <= 0 (3) 0 <= x <= 2 (4) 2 <= x <= 4 Note: "<=" means "less than or equal to" Question 2: The value of y in Question 1 above lies in the range

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Could you please help me with this problem?: Scenario: You have just graduated from college, and you have started your first big project at your new job. Your boss informs you that you are responsible for the Equations and Inequalities section of the project and for presenting your ideas to the team. Prepare for the meeting b

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** Please see the attached file for the complete problem description ** An n * n matrix A is said to be nilpotent if A^k = O for some positive integer k. Show that all the eigenvalues of a nilpotent matrix are equal to zero.

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Explain how you decide whether it is easier to solve a system by substitution or the elimination method. Response should be detailed and include an example