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System of Equations: Matrix Form and Eigenvalues

Consider the attached system of equations. (a) Write the system in the given matrix form {see attachment} (b) Determine the eigenvalues of A in terms of the parameter {see attachment} (c) The qualitative nature of solutions depends on .... (d) Sketch a typical phase portrait... Please see attachment for complete set of

Question about Fields: Complex Numbers

Please see the attached file for the fully formatted problems. LET H = a b -b a : a,b is an element of C (complex numbers) Is (H, +, .) a field? If not, give reasons.

Matrices and Vectors : Linear Independence

Please see the attached file for the fully formatted problems. Let A = [ -5, 6, -19] B= [-1, 2, -3] and C= [-2, 2, -8] Determine whether or not the three vectors listed above are linearly independent or linearly dependent. **they are linearly independent*** The vectors were written horizontally this time, as they ofte

Finding Adjoint Operators

Problem: Find the adjoint operator and its domain for: a) . (Assume is continuously differentiable and is continuous on the interval . This is the answer, I just need to see the steps to arrive there: , with boundary conditions . b) Again, here is the answer, but I need to see the solution method:

Probability that 2x2 matrix of numbers chosen from a set

Suppose that a computer program generates a matrix Where are chosen randomly from the set {-3, -2, -1, 0, 1, 2, 3}. What is the probability that the system has a unique solution? I am fairly certain that this is the case when the determinant is not zero, ie. when Using a computer script I generated all possibili

Solving Matrix Systems

Solve the System {x1 + x2 = -4 {x2 + x3 = 3 {x3 + x4 = -5 {x1 + x4 =-12 (See attachment for full question).

Matrix System Function

Solve the System { x1 - x2 - 3x3 = 6 {5x1 - 4x2 - 4x3 = 6 {2x1 + +16x3 =-36 (See attachment for full question)

Matrix Row Operations

Solve the given system using matrices (row operations). *(Please see attachment for complete problem).

Matrix Determinant

Find the determinant of the matrix... (See attachment for full question.)

Matrices : Inverses and Determinants

2. (a) Find the matrix {see attachment}, evaluate |A| and use this to find {see attachment} (b) The matrices A and B are given by {see attachment}. Find A-1 and show that B-1 does not exist {see attachment for proper citation}.

Matrix Operations and Subgroups

Let G = GLsub2 (R). a) show that T = {[a b] ad not equal to 0} is a subgroup of G {[0 d] } b) Show that D = {[a 0] ad not equal to 0} is a subgroup of G {[0 d].

Matrix Proof

Prove that ||x^(k) - x|| <= (||T||^k)(||x^(0) - x||) and ||x^(k) - x|| <= (||T||^k/(1-||T||))(||x^(1)-x^(0)||), where T is an n x n matrix with ||T|| < 1 and x^(k)=Tx^(k-1)+c, k=1,2,..., with x^(0) arbitrary, c belonging to R^n, and x=Tx+c.

Matrix Norm

The frobenius norm (which I know is not a natural norm)is defined for an n x n matrix A by ||A||_f = (sum i=1 to n, sum j=1 to n, |a_ij|^2)^1/2 Please show that ||.||_f is a matrix norm. That is, satisfy the five axioms. NOte: _ is subscript.

Important information about eigenvectors and eigenvalues

Let V be the set of real valued sequences {see attachment}. ? Check that V is a vector space over the field of real numbers, using addition of vectors {see attachment} and scalar multiplication {see attachment}. Let T be the linear shift map sending {see attachment}. ? Check that T is a linear transformation and comput