Question One a) Calculate the determinant of matrix A. Show your work in steps: A = 2013-2 - -2 1 3 2 -1 1 0 1 2 3 3-12 4 -3 1 1 3 2 0 b) Prove row linear independence is necessary and sufficient to column linear independence in the same matrix. c) Derive the inverse matrix of matrix B. Show your work in steps: [3 20 01 4 300 B = 0 0 6 5 LO 0 7 6]

Question One a) Calculate the determinant of matrix A. Show your work in steps: A = 2013-2 - -2 1 3 2 -1 1 0 1 2 3 3-12 4 -3 1 1 3 2 0 b) Prove row linear independence is necessary and sufficient to column linear independence in the same matrix. c) Derive the inverse matrix of matrix B. Show your work in steps: [3 20 01 4 300 B = 0 0 6 5 LO 0 7 6]

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter5: Business And Economic Forecasting

Section: Chapter Questions

Problem 1.4CE

See similar textbooks

Similar questions

7. Consider an n x n matrix A that is not a null matrix. Suppose that A is idempotent, and define matrix B by B = I −k²A, where ke R is a parameter. Which of the options below is the set of ALL values k such that B is idempotent? a) R b) {0} {0, 1} d) {-1,0} e) {-1,0, 1} f) {-3,0,3} g) The set of all positive whole numbers. h) None of the above.
3
Consider the data points in the table below: Y 120- Y 1.0 80.0 2.0 60 0 100- 3.0 40.0 4.0 20.0 5.0 0.0 80- Using the multipoint curve drawing tool, in the graph to the right, plot each point in the table above. Carefully follow the instructions above and only draw the required object. 60- 40- 20 0-
243 1 2 1 10 5 6 find the cofactors of the matrix
You collect the following production data for your firm: Q L 196 2 1,155 6 443 3 62 1 1,114 9 712 5 1,045 7 631 4 903 11 1,232 10 a. Which functional form (linear, quadratic, cubic) is most suitable to your data? Construct a scatter diagram but be sure to just do the dots; don’t include the lines that connect them. Then, play around with the trendline feature and include what you consider to be the best trendline. b. Using OLS, estimate the firm’s short-run production function. Comment on the strength of the regression results. c. Calculate the Q, AP, and MP for L = 8 workers. d. At 8 workers, is MC rising or falling, and how do you know?
) Suppose r is a solution to the quadratic equation r2 - 4x – 3 = 0. Find positive values for a and B such that the same a is also a solution to the cubic equation r 4. %3D ax - B = 0.
‏Solve the following LPP ‏Max Z = 8 X1 + 10 X2 + 12 X3 ‏X1 + X2> = 22 ‏X1 - X2 = N - 24 X2, ‏Where N is your Number=80 ‏X1, X2, X3> = 0 ‏ If the question can be solved by using the graphical method if it can be solved by graphical method find the value of the variables with the objective function. ‏And if it is not possible, explain the reason and suggest a method of solution. ‏Write below your final results or the conclusions you reach
5. Suppose a quadratic function is given by y = f(x) = x29x + 8. (a) Does this function represent an upward or downward facing parabola? Explain. Find the x - coordinate of the vertex (or the equation of the vertical line that intersects the parabola at the vertex) of the parabola.(b) Find the roots of the quadratic function. 1 (c) Using information from (a) and (b) draw a well labelled graph of the parabola (in particular, label the vertex and the roots).(d) In the same graph as (c), draw the parabola if it was instead represented by the function f(x) = x2-9x + 21. How many roots does this parabola have?6. Suppose an inverse demand function is given by p =10 - qd and an inverse supply function is given by p = 4+ 2qs. (a) What is the equilibrium price and quantity combination? (b) What happens when the price is above or below the equilibrium price? 7. How many solutions does a system of two equations have? Explain clearly and succinctly.
Anation with fixed quantities of resources is able to produce any of the following combinations of carpet and carpet looms: Yards of Carpet (Millions) Carpet Looms (Thousands) 75 60 20 45 35 30 45 15 50 50 These figures assume that a certain number of previously produced looms are available in the current period for producing carpet. To answer this question, assume carpet looms is on the y-axis and yards of carpet is on the x-ais The plot of these points that make up the PPF has a vertical intercept of and a horizontal intercept of This PPF would be (Enter your responses as a wvhole number) bowed out a straight line
System of Equations: p=6−2q p=2+q Plot both equations on a graph. The values of pp and qq that solve these two equations simultaneously can be seen on the graph as A. the inverse of the slopes of the two lines B. the slopes of the two lines C. the coordinates at which the two lines intersect D. the value of the intercepts of the two lines
3
Question Three Complete the following work on your own. a) Calculate the rank of the following matrix: 1 –5 2 -3 11 1 -4 2 -5 A = -1 -9 0 −4 17 5 3 6 -1 b) Calculate the rank of the following matrix and use it to determine if there exists linear dependence in this matrix: 1 6 1 0 4 4 1 B = 2 1 -9 0 3 −1 -16-1 2 22 3