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1. Assume that the field is algebraically closed and has zero characteristic, G is finite and representations are finite-dimensional.
Show that this statement is true under the above assumptions:
"Let p be an irreducible representation of G, and q be an irreducible representation of H. Is it always true that the exterior tensor product of p and q is an irreducible representation of G X H?"
2. Let p: G -> GL(V) be a representation. Show that each irreducible subrepresentation of V has multiplicity 1 iff EndG(V) is a commutative ring.
A recent article suggested that if you earn $25,000 a year today and the inflation rate continues at 3 percent per year, you'll need to make $33,598 in 10 years to have the same buying power.
Assume that n is a positive integer. Use the proof by contradiction method to prove: If 7n + 4 is an even integer then n is an even integer.
The different scenarios and their probabilities are An urn has 2 one dollar bills, one 5$ bill and one 10$ bill. A player draws one bill at a time with out replacing them until a ten dollar bill is drawn, then the game stops.
In the questions I have below it says a bowl has eight ping pong balls numbered 1,2,2,3,4,5,5,5. You pick a ball at random.
Show that if @:R -> S is a ring homomorphism, then the ker(@) is an ideal of R and that @ is injective if.
In each case, sketch the closure of the set: (pi)
What is the probability that a randomly chosen employee who has not had graduate training is a woman?
If a plant was designed to produce 7,000 hammers per day but is limited to making 6,000 hammers per day because of time needed to change equipment between styles of hammers, what is the utilization? Format as xx.x% (include the % sign.)
Show that the equation AX = B represents a linear system of two equations in two unknowns Solve the system and substitute into the matrix equation to check your results
Use the definition of the derivative to find f '(x) given Write an equation of the line tangent to the curve at the point P(-1, 7). Express the answer in the form ax + by = c.
Find an equation for the sphere, in the form of a level surface
The temperature(at a randomly selected time) is normally distributed with mean 83 degrees Fahrenheit and standard deviation 5 degrees. Find the following probabilities:
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