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Linear Algebra

Linear system

Solve the equation. Determine whether it is inconsistent, dependent, or neither. 3x - 2y = 0 9x - 8y = 7

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

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

Linear Algebra

See attached pdf file. If you have trouble displaying the math font let me know and I will try to use another format.

Linear approximation

I have another question on linear approximation using e. Suppose I want to approximate e^ 0.9. I am assuming that I let f(x) equal the following e^ 0.9 ~ e^0.5 + e^0.5 (0.9-0.5) = 0.4e^0.5 Am I on the right track?

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

Difference Equations, Transfer Functions and System Response

1. When an input x(n) = is applied to a digital filter (which is a linear system), the output is . (a) Find the transfer function of the system, (b) Find the response of the system to a sinusoidal input, Please see the attached file for the fully formatted problems.

Sequence

(See attached file for full problem description) I only need answers for 2b(ii) and 2c. Kindly show and explain all steps in details. I need step by step guidance in these questions. Please do in Mathtype and in a words document.

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