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
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- 1 1 a) Let A = 1 -1 -1 1 (i) Compute the value of det (A). (ii) For what values of x will the matrix be singular? b) Write down the quadratic form that corresponds to the following matrix. 2 4 2 -1 -3 .4 -3 1Consider the function Y5X03203, where X and Z are both greater than or equal to zero. Complete the following table by calculating the value of Y for each set of values for X and Z. X 16 18 1 8 20 16 14 N 10 6 Use the blue curve (circle symbols) to graph the values from the previous table that correspond to the contour line when Y=20. Use the green curve (triangle symbols) to graph the values from the previous table that correspond to the contour line when ya 30. Finally, use the purple curve (diamond symbols) to graph the values from the previous table that correspond to the contour line when y=40. 5 4 2 z 16 6 D 4 1 1 16 8 18 Y 0 0 10 X 12 14 10 10 20 Contour Line Y 20 N Contour Line Y 30 B Contour Line Y 40Suppose that in the country of Sudland, when the yearly rate of economic growth fell from 3.0% to 1.5%, the yearly rate of increase in airborne pollutants fell from 6% to 5%. What is the average slope of a nonlinear curve between these points using the arc method? The average slope is
- 3Given the functional relationship: y = 14x5/x2 find the value of y when x = 1.5A store owner specializes in connoisseur coffee blends and wants to make 1 kilogram bags that will sell for $ 120 using Colombian, Brazilian and Kenyan coffees. The cost per kilogram of these three types of coffee is $ 140, $ 70, $ 100, respectively. x=Colombian y=Brazilian z=Kenyan Find: The solution of the system of linear equations:
- quiz 1 (page 1 of 5) 105 econ مبادئ في الاقتصاد الرياضی ش 2 و ش elearning yu.edu.jo Question 1 Not yet answered Question 3 Marked out of 1.00 Not yet answered Marked out of 1.00 **Assume that you have the following equations: Simplify the following expression: 3X(8x+9)- X(X+7) 4P+4Q=16 2P-Q=2 The equilibrium price is: O a. 23x2 + 20X O a. P=5 O b. X2-30X O b. P=6 O c. 25X2 + 32X Oc. P-2 d. 21X2-24X O d. P-4 e. None of the above O e. None of the above Clear my choice Clear my choice Next page Next page Quiz navigation Quiz navigation 12 31 4 ...state the limitations of using a cubic function with inflection point to model the side of a hill. What assumptions have been made that may affect the reasonableness of your solutions?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
- Examine whether the following quadratic forms are positive definite, negative definite, or indefinite: (a) 6x² +25x² + 9x² − 60x2x3 + 40x1x3 – 6x1x2 - b) 9x² + 9x3 + 10x₂x3 + 6x1x27. 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.C. Suppose your neighbor is a physics major who also races motorcycles, and she tells you that horsepower can be expressed in terms of the following equation: H = MDA/S where M=mass, D-distance, A=acceleration and S and H are as defined above. Based on this conversation with your neighbor, you decide to change the functional form of the relationship to include 1/H rather than H as an explanatory variable because that's the appropriate theoretical relationship between the two variables. Estimate the above equation, substituting 1/H for H. Which of the two models do you prefer and why?