Trace inner product

Suppose V is an inner-product space. Prove that < S , T > = trace(ST*) defines an inner product on L(V).

Linear Problems

See attached file for full problem description. 1. Solve -3[5+2(-7+x)+x]=-3x-(x+3) . You must show all work to receive full credit. 2. Solve -(4x+4)/5 = (5x -1)/2 - x/3. 3. A real estate broker’s base annual salary is $18,000. She earns 3% commission on total sales. How much must she sell in real estate value during the year to earn $65,000? Set up an equation and solve. Show all work to receive full credit. Round final answer to the nearest dollar. 4. The equation d=rt represents the formula for total distance traveled. The distance traveled, d, is equal to the rate of travel, r, multiplied by the time of travel, t. Use this formula to help solve the following problem. Tina... click for more

Linear operator questions

See attached file for full problem description.

Linear functionals

Note that in problem 2, = l_1(x), etc

Polynomial Functions: Graphing different linear functions and comparing them

Your manager is very pleased with your presentations and being able to show your calculations in a detailed fashion. He has asked that you help him prepare for the upcoming company summit. Before you get together, he has asked that you give him a little review on polynomial functions and how you would apply them to everyday use. You have thought about the different methods in showing him the different methods used in calculating the functions and have drawn up an action plan. To exercise your skills, you are to perform the following using different tools available to you (e.g. Excel spreadsheet, graphing calculator, etc.) and write and explanation on your findings: The graph of: f(x)... click for more