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Question: Will focus on matrices A with the property that AT = A. show that every eigenvalue of such a matrix is necessarily real.
Let A be an n X n real matrix with the property that AT = A. Show that if Ax = λx for some nonzero vector x in Cn, then, in fact, λ is real and the real part of x is an eigenvector of A.
Compare the descriptive statistics you calculated to the population statisticsreported. Were there differences? Why or why not? Do you think that the sample you picked was representative of the population? Explain your response
Some experts estimate that the cost of education in the US increases by 6% p.a. An Ivy League college currently costs $24,502 for one year's study today. Using compound interest rate of 6% p.a, calculate the total cost of one year's tuition 6 years a..
Seawater has density 1025 kg/m3 and flows in a velocity field v=yi+xj, where x ... where x, y, and z are measured in meters and the components of v in meters per second. Find the rate of the flow outward through the hemisphere x2+y2+z2=9, z >0
Let G be the group of symmetries of a cube, including the orientation-reversing symmetries. Describe the elements of G geometrically.
Show that there can be at most one celebrity at any party and give an example of a party with no celebrities - There are two persons, X and Y. X says "At least one of us is a knave." What are X and Y?
A container in the shape of an inverted pyramid with a square base of 2 m by 2 m and height of 5 m is filled to a depth of 4 m with corn slurry. How much work is required to pump all the slurry over the top of the container?
Again, we will be going through a variety of hypothetical scenarios. For each scenario, you need to explain the reasoning behind your answer and use at least one reference from the background materials to support your answer. Overall you need to h..
find the least number of cables required to connect eight computers to four printers to guarantee that for every choice
Express the area of the triangle in terms of x only. Find A '(x). Find the critical point for x > 0. Find the maximum area of the triangle. Give an exact answer.
What are the two dollar amounts, equidistant from the mean of $30, such that 90% of all customer purchases are between these values?
Write an equation of the line through the point (4,-2) that is parallel to the line -5x+6y= -2 Write an equation of the line through the point (5,3) that is perpendicular to the line -3x+7y=5
State Rolle's Theorem. Use Rolle's Theorem to prove the Mean Value Theorem. Let f(x) = (1/5)x5 - (2/3)x3 + x. Prove that f(π) > f(1)
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