Solve the following problems by using the inverse of the matrix involved.labor hour to polish; model B(a) An automobile factory produces two models, A and B. Model A requires 1 labor hour to paint andrequires 1 labor hour for each process. During each hour that the assembly line is operating, there are 80 labor hours available forpainting and 65 labor hours for polishing. How many of each model can be produced each hour if all the labor hours available are to beutilized?(b) Suppose each model A requires 14 widgets and 10 shims and each model B requires 10 widgets and 7 shims. The factory can obtain970 widgets and 685 shims each hour. How many cars of each model can it produce while using all the parts available?(a) Model A:Model B:

(a) Given An automobiles factory produces two models A and B. Model A requires 1 labor hours to…

Answered: Solve the following problems by using…

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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Step 6. As seen in Steps 4 and 5, it takes some very special conditions, indeed, for two matrices to commute. Make up one more size 3 x 3 example. Be sure your example is different from that given in Step 4. In other words, provide two matrices A and B such that AB= BA. But, this time, make sure your matrices A and B are not diagonal. In the table below, enter your matrices A and B and verify that their products AB and BA are the same. Simplify your results as much as possible. A B АВ B BA Step 7. For this final step, let M be the set of all matrices and let D be the subset consisting of all 3 x 3 diagonal matrices. Conclusion. From the results of this and previous exercises, we have found that the set D commutative under matrix multiplication because AB = BA for matrices A and B in D By contrast, note that M commutative because AB = BA for matrices A and B in M. So, while M is not there exist subsets of M which are. And, D is just one example: can you think of others?
Determine the order of the following matrix: [[8,4,-4,9],[-4,-4,1,-3],[-6,4,-8,-8],[3,5,4,5],[8,-6,-3,3]]
Consider the following system of linear equations (SLE) 2x +y = 7 3x +2y = 12 Solve this SLE geometrically by plotting the two equations on a graph. Compose the augmented matrix corresponding to this SLE. By transforming the augmented matrix to form an echelon form matrix, solve the SLE. Detail each of the transformation steps.
At the movies, Devin bought three tickets, one drink, and one bag of popcorn for $43.75.Neil bought one ticket, three drinks, and two bags of popcorn for $27.75Jung bought two tickets, two drinks, and one bag of popcorn for $34.Determine the values that replace the letters in the augmented matrix which represents the situation.⎡⎣⎢3cea321d1∣∣∣∣b27.75f⎤⎦⎥[3�1�3��21|�27.75�] a=�= b=�= c=�= d=�= e=�= f=�= Part BUse the completed augmented matrix to find out the prices for one ticket, one drink, and one bag of popcorn. cost of one ticket = $ cost of one drink = $ cost of one bag of popcorn = $
Diagonalize the following matrix. -2 0 0 P= D= poogle Translate 0 0 -1 2 P-¹ = 0 - 3 Paraphrasing Tool ... Welcome - Realize... y https://mail.yahoo.c...
The figure to the right shows the letter L in a rectangular coordinate system. The figure can be represented by the matrix B, shown to the right. Each column in the matrix describes a point on the letter. The order of the columns shows the direction in which a pencil must move to draw the letter. The L is completed by connecting the last point in the matrix, (0,9), to the starting point, (0,0). Use these ideas to complete parts (a) and (b) below. a. If A = AB - 1 0 [!!] 0 1 find AB. (Simplify your answer.) b. Graph the object represented by matrix AB. What effect does the matrix multiplication have on the letter L represented by matrix B? Choose the correct graph below. A. O B. Rotates the letter L about the origin. Reflects the letter L across the x-axis. O C. Q 077 11 0 B-[07718] 001 199 B= Reflects the letter L across the y-axis.
A small software corporation borrowed $292,500 to expand its software line. Some of the money was borrowed at 9%, some at 10%, and some at 12%. Use a system of equations to determine how much was borrowed at each rate if the annual interest was $29,900 and the amount borrowed at 10% was 22 times the amount borrowed at 9%. Solve the system using matrices. Step 1 Let the amount borrowed at 9% be x, the amount borrowed at 10% be y, and the amount borrowed at 12% be z. The total amount borrowed was $292,500. The total annual interest was $29,900. The amount borrowed at 10% was 2- times the amount borrowed at 9%. Write a set of equations using the information given. Convert the percentage to decimal fraction. x + y + z = 292,500 .09 x +.10 y + |.12 V z = 29,900 X x - y = 0 Write the associated augmented matrix for the given system of equations. Recall that since there are three equations in the system, the matrix will have three rows. Use the coefficients of x, y and z as entries of the…
What volume of each of a 5% acid solution and a 65% acid solution should be combined to form 46 ml of a 50% solution? Set up the appropriate equations and solve the system using the inverse of the coefficient matrix. Combine O ml of the 5% acid solution withO mL of the 65% acid solution to form 46 mL of a 50% solution. (Type integers or decimals. Round the final answers to two decimal places as needed. Round all intermediate values to two decimal places as needed.)

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