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.
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.
The vectors v= -4 u = 3 and w= 4 -15 9 12 26 -15 + k -20 are linearly independent if and only if k does not equal ____?
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
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:
A=1 -1 1 0 -2 1 -2 -3 0.
A=2 -1 B=1 -2 -5 C=3 1 1 0 3 4 0 -1 0 -3 4 2 4 A. AB B. 2C-3A
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
2x+3y-2z=1 x-2y-3z=-9 5x+4y-4z=2
Y-2z=-5 5x+y-3z=15 3x+y-2z=5
If matrix A = [given], solve for the inverse matrix A-1. *(Please see attachment for complete problem)
Determine the value of K for which the system has no solutions. (See attachment for full question)
{ x + y = 6 { 4x - 2y = 42 {10x - 2y = 96 (See attachment for full question)
Solve the System {x1 + x2 = -4 {x2 + x3 = 3 {x3 + x4 = -5 {x1 + x4 =-12 (See attachment for full question).
Solve the System { x1 - x2 - 3x3 = 6 {5x1 - 4x2 - 4x3 = 6 {2x1 + +16x3 =-36 (See attachment for full question)
{ 4x1 + x2 = -9 { 12x1 + 3x2 = -27 (See attachment for full question)
Solve the given system using matrices (row operations). *(Please see attachment for complete problem).
Write the augmented matrix of the given system. *(Please see attachment for system)
Please write the given system in matrix form. *(Please see attachment for complete problem, including system and outline of the form)
Find the determinant of the matrix... (See attachment for full question.)
[-1 4 4 ][ 3] [ 0 -5 1 ][-4] = ? [ 4 1 -3 ][ 3] (See attachment for full question)
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}.
Please solve, prove and factorize the attached equations.
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].
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.
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.
Please see the attached file for full problem description. Find (f。g) (0) and (g。f) (0) Suppose
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
Please see the attached file for full problem description. --- ? Give an example of a 5x5 matrix A over the real numbers such that A has precisely three eigenvalues, 0,1 and 2 and the image of the linear transformation has dimension three. Justify your answer. ? Let V be the set of real valued sequences . Check tha
Let P = A(A^TA)^-1A^T, where A is an mxn matrix of rank n. (1) Show that P^2 = P. (2) Prove P^k = P for K = 1,2,.... (3) Show that P is symmetric. ____________________________________________________ Let AЄR^(mxn) and let r be a solution to the least square problem Ax=b. Show that a vector yЄR^n
If G ={a + b*sqrt2 | a,b rational} and H = {matrix a 2b, b a | a,b rational}, H is a 2 x 2 matrix - a 2b b a show that G and H are isomorphic under addition. Prove that G and H are closed under multiplication. I know I need to define the function map first, but I don't know what it is in this problem, let alone prove