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Consider the problem of finding an eigenvalue of an n X n matrix A when an approximate eigenvector v is known. Since v is not exactly correct, the equation
Will probably not have a solution. However, λ can be estimated by a least-squares solution when (1) is viewed properly. Think of v as an n X 1 matrix V , think of λ as a vector in R1, and denote the vector Av by the symbol b. Then (1) becomes b = λV , which may also be written as V λ = b. Find the least-squares solution of this system of n equations in the one unknown λ, and write this solution using the original symbols. The resulting estimate for λ is called a Rayleigh quotient.
A woman 5 ft tall is standing near a lamp that is 12 ft tall. Find a function that models the Length L of her shadow in terms of her distance d from the base of the lamp.
Out of these families, one is chosen at random. What is the probability that the chosen family has 1 girl?
If the gender-selection method has no effect and boys and girls are equally likely, find the mean and standard deviation for the number of boys born in groups of 51.
Find the parametric equations for the tangent line to the curve x = t^{5} - 1, y = t^{5} + 1, z = t^{3} at the point (242, 244, 27). Use the variable t for your parameter.
Which pair has equally likely outcomes? List the letters of the two choices below which have equal probabilities of success, separated by a comma.
For what value of X is the perimeter largest?
Find all maximum and minimum values of the function f(x) = 5(x^3) - 10(x^2)
Evaluate the velocity vector at a particular point, vector projection of acceleration and the length of the curve between two points.
semicircles are placed on the sides of an equilateral triangle with sides 10.1 feet. find the shaded area. with this problem the whole thing is shaded.
a new fence is constructed on three sides of a housing block with area 240m^2 the fourth side facing the road is left open. if 52 of fencing is used, what are the dimensions of the block?
suppose one test item was molded from a single batch of plastic and the hardness of this item was measured at 16 different points in time. Discuss the effect of conducting the described experiment on the error term.
You have 80 yards of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area?
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