Module 2: System of Linear Equations and Matrices

Module 2: System of Linear Equations and MatricesWeek 2 - Homework Assignment: Matrix OperationsSubmissions accepted: 6/27/2012 | 12:00 AM Review: Full, Anonymous: No Complete the following problems using your textbook:2.2 Exercise Page 86------2, 14, 22 and 282.4 Exercise Page 108------8, 16 and 362.5 Exercise Page 116------12 (Page 120 on eBook)2.2 Exercise Page 86------2, 14, 22 and 28In Exercises 1 –4, write the augmented matrix corresponding to each system of equations.2. 3x + 7y – 8z = 5 x + 3z = -24x - 3y = 7Solution:The augmented matrix will be3 7  8 5    1 0 3  2 4  3 0 7 In Exercises 9–1 8, indicate whether the matrix is in row-reduced form14. Solution: This matrix is not in row-reduced form since first nonzero entry in row 3 is a 2, not a 1.In Exercises 19–26, pivot the system about the circled element.22. Solution:Perform the operation R2 – 2R1The matrix changes to1 3 4    0  2  2Answer:1 3 4    0  2  2In Exercises 27–30, fill in the missing entries by performing the indicated row operations to obtain the row-reduced matrices.28. R2 – 2R1 – R2 R1 – 2R2 Solution:R2 – 2R1 – R2 R1 – 2R2 2.4 Exercise Page 108------8, 16 and 36In Exercises 7–1 2, refer to the following matrices:A = B = C = D = 8. Explain why the matrix A + C does not exist. A + C does not exist since dimension of matrix A is not equal to the dimension of matrix C.In Exercises 1 3–20, perform the indicated operations.16. 3 + 4 Solution:3 + 4  3 3  9  8  4 32       9 6 9   16 8 8  21  3 18  12 24 12 3  (8) 3  (4)  9  32     9 16 6  8 9  8   2112  3  24 18 12   5 1 23    25 14 17 33 21 30 5 1 23   Answer: 25 14 17 33 21 3036. INVESTMENT PORTFOLIOS The following table gives the number of shares of certain corporations held by Leslie and Tom in their respective IRA accounts at the beginning of the year:IBM GE Ford Wal-Mart Leslie 500 350 200 400 Tom 400 450 300 200Over the year, they added more shares to their accounts, as shown in the following table:IBM GE Ford Wal-Mart Leslie 50 50 0 100 Tom 0 80 100 50 a. Write a matrix A giving the holdings of Leslie and Tom at the beginning of the year and a matrix B giving the shares they have added to their portfolios.500 350 200 400 A    400 450 300 200And50 50 0 100 B     0 80 100 50  b. Find a matrix C giving their total holdings at the end of the year.C  A  B 500 350 200 400 50 50 0 100       400 450 300 200  0 80 100 50  550 400 200 500    400 530 400 250550 400 200 500 Answer: C =   400 530 400 2502.5 Exercise Page 116------12In Exercises 7–24, compute the indicated products.12. Solution: 1*1 3*3 1*3  3*0 1*0  3* 2     1*1 2*3 1*3  2*0 1*0  2* 2 10 3 6     5  3 410 3 6 Answer:    5  3 422. What is the difference between scalar multiplication and matrix multiplication? Give examples of each operation.Solution:In scalar multiplication, a number (scalar) is multiplied to a matrix and in matrix multiplication, two matrices are multiplied.Example of scalar multiplication:10 3 6 20 6 12 2      5  3 4 10  6 8 Example of matrix multiplication:10 3 6    5  3 4 1*10  3*5 1*3  3*(3) 1*6  3* 4     1*10  2*5 1*3  2*(3) 1*6  2* 4 25  6 18     0  9 2 

Module 2: System of Linear Equations and Matrices

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