Determinants and Cramer's Rule : Row Operations and Effect on Determinant, Computing Determinants and Solving Systems of 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 t ...continues

Vector Spaces, Linear Transformations, and Eigenvalues / Eigenvectors, Basis and Diagonalizing Matrices

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 ...continues

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 c ...continues

Linear Programming : Finding the Optimal Value by a Graphical Method

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. ...continues

Vector Spaces

How to prove or counter with example the following statements: (1) If two subspaces are orthogonal, then they are independent. (2) If two subspaces are independent, then they are orthogonal. I know that a vector v element of V is orthogonal to a subspace W element V if v is orthogonal to every w element W. Two subspaces W1 ...continues

Shortest Path Problem

1 a. Three cities are at the vertices of and equilateral triangle of unit length. Flying Executive Airlines needs to supply connecting services between these three cities. What is the minimum length of the two routes needed to supply the connecting service? 1 b. Now suppose Flying Executive Airlines adds a hub at the "cen ...continues

Formulate a Linear Programming model

3. The Heavy Metal Shop has four heavy presses it uses to stamp out prefabricated metal covers and housings for aviation consumer products. All four presses operate differently and are of different sizes. Currently the shop has a contract to produce three aviation products. Due to security reasons, the products are called Alpha, ...continues

Formulate a Linear Programming model

5. Bob Brown's 40th birthday party promised to be the social event of the year in Illinois. To prepare, Bob stocked up on the following liquors. Liquor On Hand (ounces) Bourbon 52 Brandy 38 Vodka 64 Dry Vermouth 24 Sweet Vermouth 36 Bob decided to mix four drinks for the party: Chaunceys, Sweet Italians, Bourbon on th ...continues

The Employee Credit Union at Directional State University is planning the allocation of funds for the coming year.

The Employee Credit Union at Directional State University is planning the allocation of funds for the coming year. ECU makes four types of loans and has three additional investment instruments. Each loan/investment has a corresponding risk and liquidity factor (on a scale of 0-100, with 100 being the most risky/liquid). The v ...continues

Network Flow Problem

(See attached file for full problem description) --- - Determine the general flow pattern in the street network shown in the diagram. ---