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Linear Algebra

Numerical Linear Algebra: Complex nxn Matrix

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.

State-Space Model

Obtain a state-space model of the system shown in Fig. 3 (see attached file).

Linear Algebra Explanation

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

College Algebra Functions and Graphs

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

Linear equations

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

Current Electricity: Kirchhoff's Laws (ully explained)

(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

Least squares solution

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?

Linear problem

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.

Numerical Linear Algebra : Unitary and Triangular Matrices and Krylov Matrix

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

Asymptotic stability of a system and Continuous Time

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

Eigenvalues : Asymptotic Stability of a System

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)

Eigenvalues, Eigenvectors and Trajectories in the Phase Plane

(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.

Systems of Differential Equations To Solve Problems

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

Exponential Random Variables with Parameters

It is known that the time (in hours) between consecutive traffic accidents can be described by the exponential r.v. X with parameter (Lambda = 1/60). Find (i) P(X < or = 60); (ii) P(X> 120); and (iii) P(10<X< or = 100).

Greatest Common Divisors

1. Let a, b be positive integers, and write a = qb + r, where q, r are Elements of Z and 0 (= or)< r < b. Suppose that d = gcd(a, b). a) If r = 0 show that d = b. b) If r > 0 show that d = gcd(b, r). 4. Use Problem 1 to find: a) gcd(100; 3); b) gcd(100; 82).

Common Divisors

1. Let d; a; b; r, and q be integers. a) Suppose that d|a and d|b. Show that d|(ra + qb). b) Suppose a = qb + r. Show that the set of common divisors of a and b is the set of common divisors of b and r.

Functions which do not converge uniformly on [0,1]

(See attached file for full problem description with proper equations) --- 9.3-3 Let . Use the result of exercise 4 of Section 9.1 to show that does not converge uniformly on [0,1], even though converges pointwise. ---