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The trace of a matrix is the sum of all its diagonal elements. Using the sub script/summation notation to represent the elements of the matrices [T ] and [M], (a) Find an expression for the trace of [T].
(b) Show that the trace of the matrix formed by the product [T][M] is equal to the trace of the matrix formed by [M][T].
forty percent of a radioactive substance decays in 5 years. By what percent does the substance decay each year?
it is desired to find two positive numbers whose sum equal 16 and whose product is to be a large as possible
63 percent of men consider themselves basketball fans. You randomly select 10 men and ask each if he considers himself a basketball fan. Find the probability that the number who consider themselves basketball fans is (a) exactly eight, (b) at leas..
the components of v 180i 450j represent the respective number of one day and three day videos rented from a video
Carry out the test in (a) at the 5% level. What is your conclusion: is the new version of the test harder than the old one? Justify your answer.
a trapezoid has an area of 80.75sq. in and its two bases are 7 and 12 inches long. find the height of the trapezoid.
Show that (Ac ∩ Bc)c = A ∪ B and (Ac ∪ Bc)c = A ∩ B. Consider rolling a six-sided die once.
Find the rate of change of the searching period with respect to temperature T. When does this rate equal zero? What (if anything) occurs when
mrs. cleaver mixes 1.24 liters of red paint with 3 times as much blue paint to make purple paint. she pours the paint
Consider the function f(x) = 7 - 3x2 on the interval [-2, 4]. Find the average or mean slope of the function on this interval, i.e. f(4)- f(-2) 4 - (-2)=?
Solve the following linear, first-order differential equations and ensure that the initial conditions are satisfied. Show whether or not the steady-state solutions are stable.
If you had to rank the eight key elements of power from most important to least, what would your list look like? In your response, be sure to explain why you thought some of the components of power were more important than the others and be sure to g..
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