Let C^2x2 be the complex vector space of 2 x 2 matrices with complex entries. Let B= [1 -1] [-4 4] and let T be the linear operator defined on C^2x2(T: C^2x2 --> C^2x2) by T(A)=BA. What is the ra
Let A = (aij ) be a complex n × n matrix. Assume that h Ax, x i = 0 for all x Є C n . Prove that (a) aii = 0 for 1 ≤ i ≤ n by substituting x = ei (b) aij = 0 for i 6 = j by substituting x = pei +qej then using (a) and putting p, q = ± 1, ± i (here i = √- 1) in various combinations Conclude that A = 0.
Let A be a symmetric and positive definite (SPD) matrix. Is A^-1 ( inverse of matrix A) a SPD matrix? If so, prove it. If not, explain and give an example.
Are the two equations the same. If so verify (see attached). σ^2 = Σ ((x[i]-bar-X)^2)/n and σ^2 = Σ (x[i]^2)/n - bar-X^2
True or false 1. Every linear system of four equations in five unknowns has infinitely many solutions. 2. If two systems of linear equations have augmented matrices that row reduce to the same reduced row echelon form, then they have the same solution set. 3. If a system of m linear equations in four unknowns has a uniq
Obtain a state-space model of the system shown in Fig. 3 (see attached file).
Hello all! I humbly apologise in advance if I'm posting inappropriately, or asking for a solution that is technically beneath you. Problem is as follows: "When Mary was half as old as Sam was when Mary was as old as Sam was when Mary was as half as old as Sam is now, Sam was four times as old as Mary was when Sam was
See attached file for full problem description.
Let A be a 3 x 3 real orthogonal matrix with det A = 1. Prove that λ= 1 is an eigenvalue of A.
Based on the parallelogram law, show that the norms ||.||_1 (1-norm) and ||.||_infinity (infinity or maximum norm) in R^2 are not induced by any inner product. Parallelogram Law: ||u+v||^2 + ||u-v||^2 = 2||u||^2 + 2||v||^2. ||x||_1: = sum i = 1 to n of |x_i| ||x||_infinity := max ( 1 =< i =< n)|x_i|.
Find two norms on the space C[0,1] that are not equivalent. Justify your answer. ( Please prove that the example you provide is a norm on the given space and show that the 2 are not equivalent.)
1. To prepare, you must perform the following tasks: The following data was retrieved from www.cdc.gov. It represents the number of deaths in the United States due to heart Disease and cancer in each of the years; 1985, 1990, 1995, and 2002. Year Disease 1985 1990 1995 2002 Heart Disease 7711
It is approximately 300 miles from Chicago, Illinois, to St. Louis, Missouri. Allowing for various traffic conditions, a driver can average approximately 60 miles per hour. How far will I need to travel to reach St. Louis after I have traveled 3 hours, and write a linear function that expresses the distance to be traveled to r
The solution to the system of equations x + 3y = 12 4x - y = -17 is: A. (3,3) B. (12, -17) C. (-3,5) D. (5,3)
An item costs $1300, has a scrap value of $100, and a useful life of six years. The linear Equation relating book value and number of years is: A. BV = -100x + 1300 B. BV = -100x + 1200 C. BV = -200x + 1200 D. BV = -200x + 1300
An item costs $900, has a scrap value of $50, and a useful life of five years. The linear equation relating book value and number of years is: A. BV = -50x + 850 B. BV = -50x + 900 C. BV = -170x + 850 D. BV = -170x + 900
Solve for x and y in the following two sets of simultaneous equations: 4x-2y = 1 ......(i) 8x-4y = 1 ......(ii) y = 2x + 3.......(i) 2y - 4x = 6 .....(ii)
(See attached file for full problem description) --- 2. Finding Unknowns Determine the unknowns in the circuit shown in Fig.3. How do electrical engineers use Kirchoff's current law and Kirchoff's voltage law to write a system of linear equations? ? Based on your explanation, write a system of linear equations for Pro
Using the least squares method answer the following in a word doc. · What are the main strengths of this method? · What are its main shortcomings? · When would least squares be useful in the real world? · Does the use of linear algebra make this method easier to understand or use?
Use the Systematic Elimination method to solve the system of ordinary differential equations. See attached file for full problem description.
I think the answer to this problem is true because 2x1 comes first and that coincides with 200. If I am wrong please explain. The question is The constraint 2x1 - x2 = 0 passes through the point (200,100). True or False.
1. Let A = QR be the factorization of a A into the product of a unitary matrix and a trianglular matrix. Suppose that the cloumns of A are linearly independent. Show that |rkk| is the distance from the k-th column of A to the linear space spanned by the first k-1 columns of A. 2. Let A Є C^(mxm) and b Є C^m be abi
6x-7y=8 -5x+2y=1
Determine the asymptotic stability of the system x' = Ax, where A is 2x2 matrix, A = alpha beta gamma delta ( that is. first row is alpha beta, second row is gamma delta) if it is known that determinant of A, det(A) = alpha*delta - beta*gamma > 0, and th
Determine the asymptotic stability of the system x' = Ax where A is 3 x 3 matrix A = -1 1 1 0 0 1 0 0 -2 ( first row is -1 1 1 second is 0 0 1 and third is 0 0 -2) More specifically, what stability conclusion(s) can be drawn? ( Justify your answer)
(i) Find eigenvalues and eigenvectors. (ii) Classify the critical point (0, 0) as to type and determine whether it is stable or unstable. (iii) Sketch several trajectories in the phase plane. Please see the attached file for the fully formatted problems.
I could really use your help on the steps and the problem. X' = (1 -1 2 -1 1 0 -1 0 1) X
Find the general solution. X' = (1 0 0 2 2 -1 0 1 0) X
Find the general solution for the following system: dx/dt = 3x - y dy/dt = 9x - 3y
Show your argument in details you can use Maple to assist you in long calculations. YOU CANNOT USE dsolve command! Consider the following system 1) Find the general solution the systems 2) Find the solution that satisfies and . Is the solution unique? 3) Plot a (the) solution of question 2). (See attached