Trace and Inner Product : Hermitian Matrices

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 ...continues

Graphs and Linear Equations

1. The following table shows the height of a tree as it ages. In Excel, plot each point on the same graph where the first coordinate is the age of the tree and the second coordinate is the height of the tree (age, height). After plotting each point, explain if there is a linear relationship between the age and height of the tr ...continues

Linear Functionals, Continuous Derivatives, Vector Spaces and Scalars

Note that in problem 2, = l_1(x), etc Please see the attached file for the fully formatted problems.

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. ...continues

Polynomial, rational, exponential and logarithmic functions and graph

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)= 0 The graph of: f(x) = a0 , where a0 ≠ 0 The graph of: f(x) = a0 + a1x , where a1 ≠ 0 For each o ...continues

Matrices, Solutions and Systems of Equations

Not all systems of linear equations have unique solutions. Before spending time trying to solve a system, it is important to establish whether it in fact has a unique solution. Matrices are the most common and effective way to solve systems of linear equations. Provide an example of a matrix that has no solution. Use row oper ...continues

Matrices - Matrix methods can be used to solve linear programming problems. For specific problems, please see the posted problems.

3-6 pages 1. Matrix methods can be used to solve linear programming problems. A linear programming problem is used to find an optimal solution, subject to stated restraints. For example, consider an accountant who prepares tax returns. Suppose a form 1040EZ requires $12 in computer resources to process and 22 minutes of the ...continues

Linear Mappings, Differentiation and Linear Spaces

1) Show that this mapping is linear: T: P5 -> P8 defined as Tp(t)=p(t+1)-p(t)+integral(t-1 to t) s^2 p(s) ds 2) Prove the following is true, or give a counterexample: If l is a nonzero scalar linear function on linear space X (which may be finite or infinite) and a is an arbitrary scalar, there exists a vector x in X st l(x ...continues

Linear Spaces, Mappings and Dimensional Spaces

1) Show that if dim X = 1 and T belongs to L(X,X), there exists k in K st Tx=kx for all x in X. 2) Let U and V be finite dimensional linear spaces and S belong to L(V,W), T belong to L(U,V). Show that the dimension of the null space of ST is less than or equal to the sum of the dimensions of the null spaces of S and T. 3) ...continues