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1. Why did Leontief use linear algebra techniques to create his model? Can you think of alternative methods?
2. What are the main strengths of his model?
3. Does it have any limitations (that you can think of)?
4. How might the Input-Output model be useful in the real world? (In other words, would anyone except an Economist be interested in the results?)
Define the function f: R → R by f(x) = x2 - 6. Briefly explain why f is not a 1-1 (one-to-one) function. Is the function g: Z → Z defined by g(n) = [n/2] a one to one function?
A credit company allocates 8-digits accounts such as 1122-3421 where the digit 1 through 9 are used. How many different account numbers can there be?
An environmental group estimates that the amount of pollution in a pond will decrease by 10% each month. To determine the concentration C, of pollutants (in parts per million) after (m) months, the group uses the function .
From the matrix S who columns are the three vectors in your basis for E3, and compute J = (S^-1)AS. Notice that if you order the columns of S in the most logical way, J will be triangular.
Which arithmetic operations on polynomials affect the values of the exponents? Can you exhibit the laws governing exponents and applications of these laws?
a rational number plus an irrational number will be ____
Determine the corresponding z -transform G(z) and the characteristic equation for this system. Using the bilinear transformation and Routh's Stability Criterion, determine the range of K for stability when the sampling time T = 0.25 s.
find the largest integer k such that the polynomial. x2 12xk can be factored into the product of two linear polynomials
Fields are an important algebraic structure, and complex numbers have that structure - verify that the fifth roots of unity form a group under complex multiplication, showing all work.
The sum of two numbers is 34. Their difference is 12. What are the two numbers?Assume the two numbers are x and y.
Determine the quadratic number fields Q[sqrt(d)] that contain a primitive nth root of unity, for some integer n.
Give an example of an exponential function. Convert this exponential function to a logarithmic function. Plot the graph of both the functions.
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