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Question: Let A be an n X n matrix, and suppose A has n real eigenvalues, λ1,,,,,,,,, λn, repeated according to multiplicities, so that
det (A - λI) = (λ1 - λ) (λ2 - λ). . .(λn - λ)
Explain why det A is the product of the n eigenvalues of A. (This result is true for any square matrix when complex eigenvalues are considered.)
Six years after purchasing shares in a mutual fund for $7800, the shares are sold for $11,100. What is the total return in percentage and the annual return in percentage?
Each side of a regular pentagon has a length of 101mm. correct to the nearest mm. What is the least possible length of each side in mm?
a) Give the exact x value of a non-stationary inflection point? b) Give an x value where the function is increasing, but concave down? c) Give an xvalue where the function is decreasing, but concave down?
(a) Rom Girard's theorem for a triangle, deduce Girard's theorem for the comp, ment of the triangle. (b) From Girard's theorem for a small triangle, deduce Girard's theorem for a tri-angle with one long edge.
1. Jackson (2012) even-numbered Chapter Exercises (p. 244). 2. What is the purpose of conducting an experiment? How does an experimental design accomplish its purpose? 3. What are the advantages and disadvantages of an experimental design in an educa..
if there are at least two varieties among the dozen donuts chosen?
Embedded Runge-Kutta Methods- Write out the formulas for k1, . . . , k4, yn+1 and y^n+1. Explain how this specific method can be implemented so that only 3 function evaluations per step are required
Given a unit line segment AB (2 cm) construct a segment of length (1+Sqrt[5])/2. Given the unit segment above and construct a segment of length Sqrt[2/3]
Create an integral whereby you are forced to use all four types of integration. Work the problem and explain why each (u-substitution, trig substitution, fractions, parts) are all needed.
Show that provided that B> -7/3, the coefficient of ε2 in the expansion of Δ is negative. What is the significance of Δ being negative - Solve Euler-Lagrange equation, and explain the significance of the solution.
State and prove the Squeeze Theorem for sequences. Use it to prove that limn→∞(n2 + n + 48769504 + sin(n)/n4 + πn2 - 2) = 0
A ranger in tower A spots a fire at a direction of 358 degrees. A ranger in tower B, located 40 mi at a direction of 58 degrees from tower A, spots the fire at a direction of 291 degrees. How far from tower A is the fire? How far from tower B?
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