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Linear Algebra

Linear system

Solve the linear system. State whether the system is inconsistent, dependent, or neither. x/6 + y/3 = 8 x/4 + y/2 = 12

System of nonlinear equations

If a system of nonlinear equations contains one equation whose graph is a circle and another equation whose graph is a line, can the system have exactly one solution? If so, what does the graph of the situation look like?

Non-linear system

The following is a non-linear system. Solve it 1/x + 2/y = 3 2/x + 1/y = 4 (Hint: Try a change in variable. Let u = 1/x ; let v = 1/y)

Linear Algebra with Cubic Roots

Exercise. IV. This problem is a partial investigation of which n×n matrices over C have cube roots; that is, for which n × n matrices A over C there is an n × n B over C such that A = B3. Since C is algebraically closed, every n × n matrix over C is similar over C to a matrix in Jordan canonical form. A. Suppose that A

Differential Equations

(See attached file for full problem description) 1) The slope field for the system dx/dt = 2x + 6y dy/dt = 2x - 2y is shown to the right a) determine the type of the equilibrium point at the origin. b) calculate all straight-line solution. 2) show that a matrix of the form A =(a b; -b a) with b!=0 must have complex eig

Pairwise Sequential Voting

A seventeen-member committee must elect one of four candidates: R, S, T, or W. Their preference schedule as shown below. Which candidate wins under pairwise sequential voting with the predetermined order S, T, W, R? Number of Members Ranking 6 R > S > T > W 5 S > R > T > W 3

Modules, Linear Operators, Characteristic & Minimal Polynomials

See the attachments. Let F be a field and . Then is an n - dimensional vector space over F. Define a function by . (a) Show that T is a linear operator. (b) Find the characteristic and minimal polynomials for T, with explanation. (For the characteristic polynomial, recall that you will need to choose a basis for

Properties of Condition Numbers : Orthogonal Matrices and Eigenvalues

Please prove the properties of condition numbers attached to this message. Refer to definitions/theorems you used. Also, if you want, have a look at the second file attached, since I believe that you can refer to the previous properties to do 6 to 10. 7. For any orthogonal matrix Q, i2(QA) = k2(AQ) = k2(A) 8. If D= diag(d1,

Linear Algebra : Use Network Analysis to Determine Number of Traffic Sensors

A traffic engineer wants to know whether measurements of traffic flow entering and leaving a road network are sufficient to predict the traffic flow on each street in the network. Consider the network of one-way streets shown in the Figure 3. The numbers in the figure give the measured traffic flows in vehicles per hour. Assume

Linear Algebra : Solving for Temperatures of Points on a Flat Square Plate

The concept of thermal resistance described in Problem 5 can be used to find the temperature distribution in the flat square plate shown in Figure 5(a). Figure 5(a) The plate's edges are insulated so that no heat can escape, except at two points where the edge temperature is heated to Ta and Tb, respectively. The temperat

Linear Algebra : Calculating heat loss through a wall

Engineers use the concept of thermal resistance R to predict the rate of heat loss through a building wall in order to determine the heating system's requirements. This concept relates the heat flow rate q through a material to the temperature difference ∆T across the material: q = . This relation is like the voltage-curr

Systems of Equations and Inequalities Applications Word Problems

1. Solve the system of equations by elimination. 7x + 8y = -55 4x + 5y = -34 2. Ron and Kathy are telemarketers. Ron contacts potential home buyers and is paid $30.00 for each buyer he gets to work with a realtor at the company. Kathy contacts potential sellers and is paid $65.00 for each seller she gets to discuss l

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 (+)

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

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

Discontinuous Counter Example

I need a counterexample for the following: If f:[a,b] -> R is ONE-TO-ONE and satisfies the intermediate value property, then f is continuous on [a,b]. I know that this is a false statement if you exclude the one-to-one property. The example I received before was f(x) = sin(1/x), but this function is not one-to-one. I am