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Linear Algebra

Non-linear Differential Equation Word Problem

Two chemicals A and B are combined to form a chemical C. The rate of the reaction is proportional to the product of the instantaneous amounts of A and B not converted to chemical C. Initially there are 40 grams of A and 50 grams of B, and for each gram of B, 2 grams of A are used. It is observed that 10 grams of C are formed

Linear algebra

Please help with the following problems. 1. Let u1 = (1,2,1,-1) and u2 = (2,4,2,0). Extend the linearly independent set {u1,u2} to obtain a basis for R4 (reals in 4 dimensions) 2. Let U1,U2 be two subspaces of a finite dimensional vector space V such that U1+U2 = V. Prove that there is a subspace W of U1 such that W (+)

Linear Functionals

(See attached file for full problem description with symbols) --- If A and B are complex matrices, show that is impossible. ---

Systems of Linear Equations, Row Echelon Form and Number of Solutions

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

State-Space Model

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

Linear Algebra

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

Numerical linear algebra/norms

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|

Numerical Linear Algebra. Norms.

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.)

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 &#1028; C^(mxm) and b &#1028; C^m be abi

Systems of Differential Equations

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

Greatest Common Divisors ( GCD )

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.