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AIOU Code 1429 Solved Assignment 2 Autumn 2022.pptx
- 1. Course: Business Mathematics (1429) Semester: Autumn, 2022 ASSIGNMENT No. 2 0314-4646739 0336-4646739 0332-4646739 Skilling.pk Diya.pk 1 Stamflay.com
- 2. Q. 1 (a) Solve the system of linear equation using matrices: X+ 2y– 3z = 1 2x – y + z = 2 x – z = 3 0314-4646739 Skilling.pk Diya.pk 2 Stamflay.com 0336-4646739 0332-4646739
- 8. (b)Can we multiply any two matrices. Explain To perform multiplication of two matrices, we should make sure that the number of columns in the 1st matrix is equal to the 0314-4646739 0336-4646739 Skilling.pk Diya.pk 8 Stamflay.com 0332-4646739
- 9. rows in the 2nd matrix. Therefore, the resulting matrix product will have a number of rows of the 1st matrix and a number of columns of the 2nd matrix. The order of the 0314-4646739 0336-4646739 0332-4646739 Skilling.pk Diya.pk 9 Stamflay.com
- 10. resulting matrix is the matrix multiplication order. Let’s learn how to multiply matrices. Consider matrix A which is a × b matrix and matrix B, which is a b ×c matrix. 0314-4646739 Skilling.pk Diya.pk 10 Stamflay.com 0336-4646739 0332-4646739
- 11. Then, matrix C = AB is defined as the A × B matrix. An element in matrix C, Cxy is defined as: Cxy=Ax1By1+….+AxbBby=∑k=1bAxkBk y 0314-4646739 0336-4646739 Skilling.pk Diya.pk 11 Stamflay.com 0332-4646739
- 12. For x = 1…… a and y= 1…….c This is one of the most important topics in class 12. Matrices for class 12 explains the types of matrices in detail. 0314-4646739 0336-4646739 Skilling.pk Diya.pk 12 Stamflay.com 0332-4646739
- 13. Notation If A is a m×n matrix and B is a p×q matrix, then the matrix product of A and B is represented by: X = AB 0314-4646739 0336-4646739 Skilling.pk Diya.pk 13 Stamflay.com 0332-4646739
- 14. Where X is the resulting matrix of m×q dimension. 0314-4646739 0336-4646739 Skilling.pk Diya.pk 14 Stamflay.com 0332-4646739
- 15. Matrix Multiplication Formula Let’s take an example to understand this formula. Let’s say A and B are two matrices, such that, 0314-4646739 0336-4646739 Skilling.pk Diya.pk 15 Stamflay.com 0332-4646739
- 17. Algorithm for Matrix Multiplication There has been a significant amount of work in recent years in the field of matrix multiplication algorithms as it has found its 0314-4646739 0336-4646739 Skilling.pk Diya.pk 17 Stamflay.com 0332-4646739
- 18. application in many areas. There are four types of algorithms: Iterative Algorithm Divide and conquer algorithm Sub-cubic algorithms 0314-4646739 0336-4646739 Skilling.pk Diya.pk 18 Stamflay.com 0332-4646739
- 19. Parallel and distributed algorithms This is majorly used in various programming languages such as C, Java, etc., for online multiplication. The most 0314-4646739 0336-4646739 Skilling.pk Diya.pk 19 Stamflay.com 0332-4646739
- 20. common are 2×2, 3×3 and 4×4, multiplication of matrices. The operation is binary with entries in a set on which the operations of addition, subtraction, multiplication, and division are 0314-4646739 0336-4646739 0332-4646739 Skilling.pk Diya.pk 20 Stamflay.com
- 21. defined. These operations are the same as the corresponding operations on real and rational numbers. Although there are many applications of matrices, essentially, multiplication of 0314-4646739 0336-4646739 Skilling.pk Diya.pk 21 Stamflay.com 0332-4646739
- 22. The linear mapping, which includes scalar addition and multiplication, is represented by matrix multiplication. 0314-4646739 0336-4646739 0332-4646739 matrices is an operation in linear algebra. Skilling.pk Diya.pk 22 Stamflay.com
- 23. One can also find a wide range of algorithms on meshes. This type of algorithm is designed to minimize the inherent inefficiency of standard array algorithms 0314-4646739 0336-4646739 0332-4646739 Skilling.pk Diya.pk 23 Stamflay.com
- 24. where there can be a delay in the arrival of data from 2 different matrices. 0314-4646739 0336-4646739 Skilling.pk Diya.pk 24 Stamflay.com 0332-4646739
- 25. Matrix multiplication Rules From the above defined formula and procedure, we can write the following rules and properties for matrix multiplication. 0314-4646739 0336-4646739 Skilling.pk Diya.pk 25 Stamflay.com 0332-4646739
- 26. The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B. If AB is defined, then BA need not be defined 0314-4646739 0336-4646739 Skilling.pk Diya.pk 26 Stamflay.com 0332-4646739
- 27. If both A and B are square matrices of the same order, then both AB and BA are defined. If AB and BA are both defined, it is not necessary that AB = BA. 0314-4646739 0336-4646739 Skilling.pk Diya.pk 27 Stamflay.com 0332-4646739
- 28. If the product of two matrices is a zero matrix, it is not necessary that one of the matrices is a zero matrix. 0314-4646739 0336-4646739 Skilling.pk Diya.pk 28 Stamflay.com 0332-4646739
- 29. Q. 2 The shifts in population within annual three provinces of a country is given by: 0314-4646739 Skilling.pk Diya.pk 29 Stamflay.com 0336-4646739 transition matrix of 0332-4646739
- 30. i.Determine whether the population will attain an equilibrium condition. ii.Find the relative population shares of the three provinces. 0314-4646739 Skilling.pk Diya.pk 30 Stamflay.com 0336-4646739 0332-4646739
- 32. Hence from the above calculations it is verified that the population will attain an equilibrium condition. Q. 3 0314-4646739 0336-4646739 Skilling.pk Diya.pk 32 Stamflay.com 0332-4646739
- 35. (ii) Skilling.pk Diya.pk 35 Stamflay.com 0314-4646739 0336-4646739 0332-4646739
- 38. Q. 4 Skilling.pk Diya.pk 38 Stamflay.com 0314-4646739 0336-4646739 0332-4646739
- 39. (a)Determine the location of all critical points and determine their nature for the function. (i) f(x) = – 100e–0.25x – 50x 0314-4646739 0336-4646739 Skilling.pk Diya.pk 39 Stamflay.com 0332-4646739
- 40. f'(x)=0.25*e^(-0.25x)-50 0314-4646739 Skilling.pk Diya.pk 40 Stamflay.com 0336-4646739 0332-4646739
- 41. set equal to 0. 50=25e^(-0.25x) 2=e^(-0.25x) ln 2=-0.25x 0.693=-0.25x 0314-4646739 0336-4646739 Skilling.pk Diya.pk 41 Stamflay.com 0332-4646739
- 42. x=-2.77 f(x)=-61.37 second derivative is -6.25e^(-0.25x) where x=-2.77 the second derivative is negative. This is a maximum. 0314-4646739 0336-4646739 Skilling.pk Diya.pk 42 Stamflay.com 0332-4646739
- 43. (b) Given the demand function q1= f(p1, p2) = 36,000 - 0.1p2 0.5 p2 1 2 i.Determine the partial derivatives fp1 and fp2 0314-4646739 0336-4646739 Skilling.pk Diya.pk 43 Stamflay.com 0332-4646739
- 44. Let p1 =x p2 = y 0314-4646739 Skilling.pk Diya.pk 44 Stamflay.com 0336-4646739 0332-4646739
- 46. Now w.r.t y 0314-4646739 Skilling.pk Diya.pk 46 Stamflay.com 0336-4646739 0332-4646739
- 49. ii. If p1 = 20 and p2 =10, evaluate fp1 and fp2 and interpret their meaning. 0314-4646739 Skilling.pk Diya.pk 49 Stamflay.com 0336-4646739 0332-4646739
- 50. yz 2 2x2 xy Q. 5 (a) Find fx, fy, fz, fyx, fxz, fzy, fy, (2, –1, 3), fyz, (–1, 1, 0). if f(x, y, z) = fx = 0314-4646739 Skilling.pk Diya.pk 50 Stamflay.com 0336-4646739 0332-4646739
- 52. fy = 0314-4646739 Skilling.pk Diya.pk 52 Stamflay.com 0336-4646739 0332-4646739
- 55. fz = 0314-4646739 Skilling.pk Diya.pk 55 Stamflay.com 0336-4646739 0332-4646739
- 57. fyz = 0314-4646739 Skilling.pk Diya.pk 57 Stamflay.com 0336-4646739 0332-4646739
- 60. fyx = 0314-4646739 Skilling.pk Diya.pk 60 Stamflay.com 0336-4646739 0332-4646739
- 62. fzy = Skilling.pk Diya.pk 62 Stamflay.com 0314-4646739 0336-4646739 0332-4646739
- 66. (b) Suppose z = f (x, y) describes the cost to build a certain structure, where x represents the represents the labor costs and y cost of materials. Describe what fx and fy represent. 0314-4646739 0336-4646739 Skilling.pk Diya.pk 66 Stamflay.com 0332-4646739
- 67. Basically fx and fy represents the marginal labour cost and marginal cost of materials respectively. fx and fy are calculated by taking partial derivatives of z. 0314-4646739 0336-4646739 Skilling.pk Diya.pk 67 Stamflay.com 0332-4646739