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Linear Algebra

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.


(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

Eigenvectors from Transformations : Reflection, Shear and Rotation

In each part find as many linearly independent eigenvectors as you can by inspection (by visualizing the effect of the transformation of R^2). For each of your eigenvectors, find the corresponding eigenvalue by inspection; then check your results by computing the eigenvalues and bases for the eigenspaces from the standard matrix


Find the eigenvalues of the following matrix [0 0 1 ] [1 0 w+1+1/w ] [0 1 -w-1-1/w ] where w = e^(2 pi i/3) Please see the attached file for the fully formatted problem.

Bounded Linear Operator and Norm

Let . Define . Show that defines a bounded linear operator on when is a continuous function on . Also, estimate the norm of T. Please see the attached file for the fully formatted problems.

Linear Algebra

I'm having a hard time with this problem. Please help me. Also, please be detailed so that I can understand how the problems were solved. Let A = ( ) be an n n matrix. Define a trace of A to be the sum of the diagonal elements, that is tr(A) = . (a) Show that the trace is a line

Linear Algebra : Linear Maps and Kernel

Let L: V W be a linear map. Let w be an element of W. Let be an element of V such that L( ) = w. Show that any solution of the equation L(X) = w is a type , where u is an element of the kernel of D? Please see the attached file for the fully formatted problem.

Linear Algebra

I would really appreciate some help on these problems. I really need to understand how to do these proofs. So, please be detailed. 1. Let V be a vector space and F: V R a linear map. Let W be the subset of V consisting of all elements v such that F(v)=0. Assume that W V, and let be an element of V which does not lie in

Solving a System of Differential Equations

1. Consider the initial-value problem dx/dt = A(f,u)x, x(0) =[0] [1] where A(f,u)= [ -f 1] [ 0 -u] where f and u are positive parameters. Solve it if u does not equal f

Linear Algebra and Matrices : Determinant Functions

Let R be the field of real numbers, and let D be a function on matrices over R, with values in R, such that Suppose that . (a) Prove that . (b) if (c) if B is obtained by interchanging the rows (or columns) of A.

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

Applications of Linear Equations : A Quick Setting Grout

A quick setting grout made from a mixture of cement/sandwater and an additive is needed for a tunnelling project Two trial mixes have been made with the following combinations of grout and additive. 5 litres of sand/cement/water + 1 litre of additive =6 liter of grout mass=12.487kg 5 liters of sand/cement/water =1.5lit