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Let G = UT (n,F) be the set of the upper triangular n x n matrices with entries in a field F with p elements and 1's on the diagonal. The operation in G is matrix multiplication.
(a) Show that G is a group
(b) Show that G is a finite p-group
(c) Consider the upper central series of G:1 = Z_0 (G) <= Z_1 (G) <= Z_2 (G) <=....<= Z_c (G) = G
Write explicitly what Z_1 (G), Z_2 (G), and Z_3 (G) are.
Show that Z_3 / Z_2 = Z (G/Z_2)
Prove that G is nilpotent of class exactly n-1.
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Write an equation of the line containing the given point and perpendicular to the given line. Express your answer in the form y=mx+b
Suppose the Phillips curve is represented by the following: πt = πte + 0.20 - 2ut where πte = θπt=1. Assume θ = 0.8, πt=1 = 0.10 (10%) and ut = 0.05 (5%). Calculate πt.
Find the least squars solution of Ax=b, retaining five places to the right of the decimal point. Finally, verify that your least squares solution satisfies the least-squares problem and calculate the normalized error e=E/ lbl.
Solve the equations by using addition or substitution method.
SAS (pronounced "sass"), which is short for Statistical Analysis System, began when it set out to create statistical software to help agricultural researchers who were studying the effects of soil, seeds, and the weather on crop yields. In 1970, rese..
Find how many of each brand should the store stock
Conversely, suppose A and A^-1 are both matrices with integer entries. Prove that D(A_1, A_2) = +/- 1.
During a road trip, Tonya drove one-third the distance that Lana drove. Mark drove 15 miles more than Lana. The total distance they drove on the trip was 491. How many miles did each person drive?
What computer applications can be used to graph systems of equations? In what circumstances does it make more sense to graph a system than to use the substitution, elimination, or matrix methods?
create an equation you could use to calculate the cost one person spends on food for a year assume no tax on the food
A merchant mixed 10 lb of cinnamon tea with 5 lb of spice tea. The 15 pound mixture sells for $40. A second mixture includes 12 lb of cinn tea and 8 lbs of spice tea. The 20 lbs mixture sells for $54. Find the cost per lb of the cinn tea and the s..
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