Systems of Linear Equations

(See attached file for full problem description with complete equations) --- 1. Find the augmented matrix for each system of linear equations: a. 5x1 + 7x2 + 8x3 = 3 -2x1 + 4x2 + 9x3 = 3 3x1 - 6x2 + x3 = 1 b. 4x1 + x2 - 7x3 = 6 5x1 + 7x2 + 2x3 = 3 5x1 + 2x2 + 5x3 = 7 c. 3x1 - 2x2 + 2x3 = 7 5x1 + 7x2 + 3x3 = 3 -5x1 + 6x2 - 8x3 = -5 2. Using elementary row operations reduce each of the augmented matrices from Problem 1 to reduced echelon form 3. Using the information from Problem 2, what are the solutions to the system of linear equations 4. Indicate whether the following statements are True or False a. Elementary row operations on an augmented matrix never chan... click for more

Determinants and Cramer's Rule

(See attached file for full problem description with complete equations) --- 1. State the elementary row operation being performed and its effect on the determinant Start with matrix a b c d a. c d a b b. a b kc kd c. a + kc b + kd c d 2. Compute the determinant a. 3 0 4 2 3 2 0 5 -1 b. 1 3 5 2 1 1 3 4 2 c. 3 5 -8 4 0 -2 3 -7 0 0 1 5 0 0 0 2 3. Use row reduction to convert the matrices to echelon for and then compute the determinant of each matrix a. 1 3 0 2 -2 -5 7 4 3 5 2 1 1 1 2 -3 b. 1 -1 -3 2 0 1 5 4 -1 2 8 5 3 -1 -2 3 c. 1 3 -1 0 -2 0 2 -4 -1 -6 -2 -6 2 3 9 3 7 -3 8 -7 3 5 5 2 7 4. Use Cramer's Rule to compute solutions to the followin... click for more

Vector Spaces, Linear Transformations, and Eigenvalues/Eigenvectors

(See attached file for full problem description with equations) --- 1. Answer the following questions A. Is lambda = 2 an eigenvalue of the following matrix? Why or why not? 3 2 3 8 B. Is lambda - -2 an eigenvalue of the following matrix? Why or why not? 7 3 3 -1 C. Is the following vector an eigenvector of the following matrix? If so, find the eigenvalue. 1 4 -3 1 -3 8 2. Find a basis for the eigenspace corresponding to each listed eigenvalue and the following matrix a. lambda = 1, 5 5 0 2 1 b. lambda = 4 10 -9 4 -2 3. Find the eigenvalues of the following matrices a. 0 0 0 0 2 5 0 0 -1 b. 4 0 0 0 0 0 1 0 -3 4. In the following problem, A is an n x n (... click for more

Linear Programming to minimize costs

See attached file for full problem descriptions with complete equations. --- 1. During the next three months, Ironco faces the following demands for steel: 100 tons (month 1); 200 tons (month 2); 5 tons (month 3). During any month, a worker can produce up to 5 tons of steel. Each worker is paid $5000 per month. Workers can be hired or fired at a cost of $3000 per worker fired and $4000 per worker hired (it takes 0 time to hire a worker). The cost of holding a ton of steel in inventory for one month is $100. Demand may be backlogged at a cost of $70 per ton month. That is, if 1 ton of month 1 demand is met during month 3, then a backlogging cost of $140 is incurred. At the beginni... click for more

Linear Programming

(See attached file for full problem description) --- 1. AA Auto manufactures luxury cars and trucks. The company believes that its most likely customers are high-income women and men. To reach these groups, AA Auto has embarked on an ambitious TV advertising campaign and has decided to purchase 1-minute commercial spots on two types of programs: comedy shows and football games. Each comedy commercial seen by 7 million high-income women and 2 million high-income men. Each football commercial is seen by 2 million high-income women and 12 million high-income men. A 1-minute comedy ad costs $50,000.00 and a 1-minute football ad costs $100,000.00 AA would like the commercials to be seen... click for more