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#S Matrix A has the dimensions 6 x 2 and Matrix B has the dimensions 3 x 3. What are the dimensions of the product AB?

#S Matrix A has the dimensions 6 x 2 and Matrix B has the dimensions 3 x 3. What are the dimensions of the product AB?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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As part of your preparation, you should start by writing the relevant formulas for each of the types of questions and prepare your formula sheet. Your formula sheet can be an 8 1/2 x 11 sheet of paper, double-sided. NO examples, only steps and formulas. Next, identify for each question which type of problem it is. You may want to mark the problems. Now you are ready to DO the problems. Happy studying! #1 Without any computations, identify whether each of the equations is recursive or explicit. A. x₂ = 7(1.7)" B. X=X-₁+4 C. Xn = 1.7xn-1 Xn=7n+4 D. E. X = 1.7xn-1 +4 #2 You are given the recursive equation of a linear DDS that describes the size of a population P₁, after n years with initial value Po = 150. How would you compute Ps4, the size of the population after 54 years? There are multiple ways to solve the problem. Select all correct choices. A. Use the recursive DDS equation and substitute n = 55 B. Use the recursive DDS equation and substitute values of P, for a total of 54 steps Use the explicit solution and substitute P = 150 and n = 54 Use the explicit solution and substitute P₁ = 150 and n = 55 C. D. E. Use the recursive DDS equation, substitute the value of Po, and compute one iteration #3 The solution of a system of linear equations in the variables x,y,z, and u using the Gauss-Jordan method is represented by the following augmented matrix: [100 11 0103 -7 0017 -14 Loo 00 0 a) Write the general solution for this system in terms of the variable u. (Hint: Your answer should give .x, y, and zin terms of u ). (x,y,z,u) = b) Write the specific solution for this system as a 4-tuple when u = 2. (x,y,z,u) =
Transcribed Image Text:As part of your preparation, you should start by writing the relevant formulas for each of the types of questions and prepare your formula sheet. Your formula sheet can be an 8 1/2 x 11 sheet of paper, double-sided. NO examples, only steps and formulas. Next, identify for each question which type of problem it is. You may want to mark the problems. Now you are ready to DO the problems. Happy studying! #1 Without any computations, identify whether each of the equations is recursive or explicit. A. x₂ = 7(1.7)" B. X=X-₁+4 C. Xn = 1.7xn-1 Xn=7n+4 D. E. X = 1.7xn-1 +4 #2 You are given the recursive equation of a linear DDS that describes the size of a population P₁, after n years with initial value Po = 150. How would you compute Ps4, the size of the population after 54 years? There are multiple ways to solve the problem. Select all correct choices. A. Use the recursive DDS equation and substitute n = 55 B. Use the recursive DDS equation and substitute values of P, for a total of 54 steps Use the explicit solution and substitute P = 150 and n = 54 Use the explicit solution and substitute P₁ = 150 and n = 55 C. D. E. Use the recursive DDS equation, substitute the value of Po, and compute one iteration #3 The solution of a system of linear equations in the variables x,y,z, and u using the Gauss-Jordan method is represented by the following augmented matrix: [100 11 0103 -7 0017 -14 Loo 00 0 a) Write the general solution for this system in terms of the variable u. (Hint: Your answer should give .x, y, and zin terms of u ). (x,y,z,u) = b) Write the specific solution for this system as a 4-tuple when u = 2. (x,y,z,u) =
#4 According to data from a Texas agricultural report, the amount of nitrogen (in lbs/acre), phosphate (in lbs/acre), and labor (in hr/acre) needed to grow honeydews, yellow onions, and lettuce is given in the following table. Source: The AMATYC Review. Nitrogen Phosphate Labor Phosphate (in lbs): Labor (in hours): Honeydews 120 180 4.97 Let h = # of acres of honeydew, y = # of acres of yellow onions, and I = # of acres of lettuce planted. Assuming that the farmer has 27100 lbs of nitrogen, 28500 lbs of phosphate, 485 hours of labor, and 190 acres available for planting, write down a system of equations for the resources. Nitrogen (in lbs): Acreage (in acres): Yellow Onions 150 80 4.45 Lettuce 180 80 4.65 #5 Matrix A has the dimensions 6 x 2 and Matrix B has the dimensions 3 x 3. What are the dimensions of the product AB ? #6 A population follows a logistic DDS given by Pn = 1.165pm-1-0.00021p²-1 a) Determine the growth rater. Round to three decimal places. b) Determine the carrying capacity. Round to the nearest integer value. c) State the equilibrium values for this population. Round to the nearest integer value.
Transcribed Image Text:#4 According to data from a Texas agricultural report, the amount of nitrogen (in lbs/acre), phosphate (in lbs/acre), and labor (in hr/acre) needed to grow honeydews, yellow onions, and lettuce is given in the following table. Source: The AMATYC Review. Nitrogen Phosphate Labor Phosphate (in lbs): Labor (in hours): Honeydews 120 180 4.97 Let h = # of acres of honeydew, y = # of acres of yellow onions, and I = # of acres of lettuce planted. Assuming that the farmer has 27100 lbs of nitrogen, 28500 lbs of phosphate, 485 hours of labor, and 190 acres available for planting, write down a system of equations for the resources. Nitrogen (in lbs): Acreage (in acres): Yellow Onions 150 80 4.45 Lettuce 180 80 4.65 #5 Matrix A has the dimensions 6 x 2 and Matrix B has the dimensions 3 x 3. What are the dimensions of the product AB ? #6 A population follows a logistic DDS given by Pn = 1.165pm-1-0.00021p²-1 a) Determine the growth rater. Round to three decimal places. b) Determine the carrying capacity. Round to the nearest integer value. c) State the equilibrium values for this population. Round to the nearest integer value.
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