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A Householder matrix, or an elementary reflector, has the form Q = I - 2uuT where u is a unit vector. Show that Q is an orthogonal matrix. (Elementary reflectors are often used in computer programs to produce a QR factorization of a matrix A. If A has linearly independent columns, then left-multiplication by a sequence of elementary reflectors can produce an upper triangular matrix.)
A man rows a boat 480 feet upstream against a constant current in 8 minutes. He then rows 210 feet downstream ( with the same current) in 3 minutes. Find the speed of the current and the equivalent rate at which he can row in still water.
Find the distance form the base of the pole to the guy wires point of attachment.
Dividing a complex number with another number.
"True/False. If B is similar to a diagonal n*n matrix D with diagonal entries a1 , a2 , ... , an , then det B = a1a2 ... an (prod of diag entries)"
Maximize and minimize p = 2x-y with respect to x+y ≥ 2, x+y ≤ 10, x-y ≥ -2 and x-y ≤ 2. (Draw the lines, shade out a feasable region, look at boundary points)
A printer has a contract to print 100,000 invitations for a political candidate. He can run the invitations by using any number of metal printing plates from 1 to 20 on his press.
A retailer finds that the demand for a very popular board game averages 100 per week with a standard deviation of 20. If the seller wishes to have adequate stock 95% of the time, how many of the games must she keep on hand?
To check the Ace company's claim that the total of their 2,300 accounts receivable was $1,081,000 and that the standard deviation of the individual accounts was $ 210 the external auditor took a sample of 25 accounts which totalled $9,900.
dim(ker(A-3I)^2)=4 dim(ker(A-3I)^3)=5 What is the characteristic polynomial of A? what is the minimal polynomial of A?
An open box having a volume of 162 in.3 is to be constructed. If the box is to include a partition that is parallel to a side of the box, as shown in the figure, and the amount of material used is to be minimal, what should be the dimensions of th..
Estimate the relative error in the calculated surface area.
F ind the probability that the mean of the number of hours they watch television will be greater than 27.3 hours. Give your answer to 2 decimal places.
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