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
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
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
1. An electrical circuit is shown in Figure 1. Figure 1 The governing KVL and KCL equations are: v-R2i2-R4i4 = 0; -R2i2+R1i1+R3i3 = 0; -R4i4 -R3i3+R5i5 = 0 i6 = i1+i2; i2 +i3 = i4; i1 = i3+i5; i4+i5 = i6 Find the currents for the case: R1 = 1 k; R2 = 5 k; R3 = 2 k; R4 = 10 k; R5
Please help to find the answer for cos(x) in the following equation, showing all the steps. d²y/dx² + y = cosx.
Let A be a square matrix such that A^3 = A. What can you say about the eigenvalues of A?
See the attached file. 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
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.
Find the eigenvalues of the matrix: [c1 c2....cn] [c1 c2....cn] [c1 c2....cn] [...............] Please see the attached file for the fully formatted problem.
Verify example 14.15 (attached) i.e; first solve the system by LU decomposition without pivoting, using beta= 10, and t=2,3 respectively. Then solve the system with partial pivoting, using beta = 10, and t= 2,3 respectively. Please I want a detailed solution so I can do such problems in the future. Thanks.
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.
11.8 Let and where a "1" appears in the n-th position and a zero in all other positions. Let (an) be a sequence of complex numbers. Prove then that (i) ... defines a bounded linear operator on G if and only if... , and accordingly find the norm of T. (ii) What are the necessary and sufficient conditions for T to be
[ I0*(Rvia/Lt) Ko(Rvia/Lt) ] [A] = [V0] [ (1/Lt)*I1*(Rcon/Lt) -(1/Lt)*K1*(Rcon/Lt)] * [B] [ 0] Above is a matrix that I am trying to solve A and B for. What are A and B? and how did you find them? Thanks.
Please help with the following problem. 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 linear map of the space
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.
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 W. Sho
Let a_1, a_2, ... , a_n and b_1, b_2, ... , b_n are elements in a field F. Let A be an n x n matrix with 1/ a_1 + b_1 in row i, column j. Find the det(A).
1) An open-top box is to be constructed from a 4 by 6 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out. a) Find the function V that represents the volume of the box in terms of x. Answer: b) Graph this funct
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.
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
See the attached file. Now let V be the space of all 2x2 matrices over the field F and let P be a fixed 2x2 matrix. Let T be the linear operator on V defined by T(A) =PA. Prove that tr(T)=2tr(P). From a previous exercise we know that similar matrices have the same trace. Thus we can define the trace of a linear operator o
Let β = {α1, α2, α3} be the basis for (complex) (C^3) defined by α1=(1,0-1), α2=(1,1,1), α3=(2,2,0). Find the dual basis of β showing all work. Please see the attached file for the fully formatted problems.
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
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
3. Let B1 = {v1,v2,v3} be a basis of vector space V and B2 = {w1,w2,w3} where w1=v2+v3; w2=v1+v3; w3= v1+v2 Verify that B2 is also a basis of V and find the change of basis matrices from B1 to B2 and from B2 to B1. Express the vector a(v1) +b(v2) + c(v3) as a linear combination of w1,w2,w3
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 (+)
(See attached file for full problem description with symbols) --- If A and B are complex matrices, show that is impossible. ---
Please help me solve the following system of three equations and discribe the methods that are being used to help me understand: X + Y + Z = 6 2X - Y + 3Z = 8 3X - 2Y - Z = -17 Thank you!
Please see the attached file for the fully formatted problems.
1. Solve this system of equations. Put your answer in alphabetical order. 5w+3x-y-z=-2 w+x+y+z=2 2W-x+y+4z=0 3w+2x+3y+2z=1 2. If x varies directly as 2y-1, and x=9 when y=2, find the value of y when x has a value of 15.