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Let V be a , but with the weighted inner product, ,,where and . Let be the linear transformation given by T(a,b,c)=(3a-2c,b,3a+10c).
a. Show that T can be diagonalzed and find a basis for V comprised of eigenvectors of T.
b. Find the matrix of the adjoint of T with respect to the basis .
Suppose that the number of cars, C, on 1st Avenue in a city over a period of time t, in months, is graphed on a retangular coordinate system where time is on the horizontial axis.
Jack and Jill went up the hill and found that their grandmother had died. She left them in her will only one possession: an antique water pail.
Write an equation that models how old in years each of you will be, when your ages add up to 150 years old. For example, if x = your age and the eldest person was a year older than you,
A company produces the financial results shown in the table below. The executives at the firm have good reason to believe that $10 million in sales will be generated in 2010.
Find the dimension of the solution space of the following homogenous system of linear equations
Create a proof by mathematical induction that demonstrates that the sum of the first n even numbers is equal to n(n + 1)
use the factor theorem to determine whether x - c is a factor of f. if it is write f in factored form that is write f
A personality test has a subsection designed to assess the "honesty" of the test-taker. Suppose that you are interested in the mean score, mu, on this subsection among the general population.
Solve algebraically and check your potential solutions
In 1990 the life expectancy of males in a certain country was 61.2 years. In 1996 it was 64.3 years. Let E represent the life expectancy in year t and let + represent the number of years since 1990.
Suppose [a]m (m is a subscript) represents an equivalence class modulo m, where m is an integer. Prove that for any two integers a and b that, under multiplication, [a]m[b]m = [ab]m.
How do we determine if two lines are parallel, perpendicular, or intersecting? First of all, you know that two lines are parallel if they never touch, so if they are parallel, then they are neither perpendicular nor intersecting.
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