(a) Explain why the incidence matrix for a disconnected graph can be written in block diagonal matrix...

Question:

(a) Explain why the incidence matrix for a disconnected graph can be written in block diagonal matrix form

under an appropriate labeling of the vertices.
(b) Show how to label the vertices of the digraph in Exercise 2.6.3e so that its incidence matrix is in block form.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Applied Linear Algebra

ISBN: 978-0131473829

1st edition

Authors: Peter J. Olver, Cheri Shakiban

See More Books

Question Posted: Jun 17, 2016 08:35 AM

See More Questions

Show that if p0i = 1/k for i = 1, . . . , k, then the statistic Q defined by Eq. (10.1.2) can be written in the form ) . i=1
Show that the fourth-order Runge-Kutta method, k1 = hf (ti ,wi), k2 = hf (ti + h/2,wi + k1/2), k3 = hf (ti + h/2,wi + k2/2), k4 = hf (ti + h,wi + k3), wi+1 = wi + 1/6 (k1 + 2k2 + 2k3 + k4), when...
A connected graph is called a tree if it has no circuits. (a) Find the incidence matrix for each of the following directed trees: (i) (ii) (iii) (iv) (b) Draw all distinct trees with 4 vertices....
The OrbitTrack Company specializes in developing and selling a wide range of high-quality scooters. Sales representatives report that there is a growing demand for racing scooters. OrbitTrack's...
What is a project portfolio management system? How would you justify the investment in such a system?
Fisico Company produces exercise bikes. One of its plants produces two versions: a standard model and a deluxe model. The deluxe model has a wider and sturdier base and a variety of electronic...
A filament-wound E-glass/epoxy pressure vessel has a diameter of 50 in. (127 cm), a wall thickness of 0.25 in. (6.35 mm), and a helical wrap angle = 54.74. Using a netting analysis and a safety...
Sippy was thinking of buying Christichs house. He noticed watermarks on the ceiling, but the agent showing the house stated that the roof had been repaired and was in good condition. Sippy was not...
1. (18 Total Points) Suppose that two players are playing the following game. Player 1 can choose either Top or Bottom, and Player 2 can choose either Left or Right. The payoffs are given in the...
Stock A has an expected return of 7%, a standard deviation of expected returns of 35%, a correlation coefficient with the market of 20.3, and a beta coefficient of 20.5. Stock B has an expected...
True or false: If A and B are incidence matrices of the same size and coker A = coker 5. then the corresponding digraphs are equivalent.
(a) Draw the graph corresponding to the 6 7 incidence matrix whose nonzero (/, j) entries equal 1 if j = i and - 1 if j = i + 1, for i = 1 to 6. (b) Find a basis for its kernel and cokemel. (c) How...
An accountant is a professional who can plan, direct, and evaluate a clients financial affairs. True/False
In the acrolein process introduced in problem 15.1, the catalyst is packed in tubes and the reactor is cooled using a circulating molten salt. The molten salt rejects heat to boiling steam in a...
As in the situation illustrated in Figure 2.16, an Irish Web design project at day 70 exhibits only 35 percent progress when 40 percent was planned, for an effective date of 55. Planned value was ...
Explain briefly the relationship between materiality limits, audit risk and audit planning.
Exactly what decreases in unit cost occur with larger facilities as a result of economies of scale? Might any costs increase with the size of a facility?
Over the last quarter, 742 shots were administered at a walk-in clinic. To be treated properly, patients must be given the correct dosage of the correct medication. During the quarter in question, it...
Compare and contrast the receipt of cash from a charge customer with the receipt of cash at the time of the merchandise sale.
CdF2 (s) Cd+ (aq) + 2 F- (aq) 1. A saturated solution of CdF2 is prepared. The equilibrium in the solution is represented above. In the solution [Cd+] eq = 0.0585 M and [F-] eq = 0.117 M. a....
If N(A) = (0), then the system Ax = b will have a unique least squares solution.
If Q1 and Q2 are orthogonal matrices, then Q1Q2 is also an orthogonal matrix.
If {u1, u2,..., uk} is an orthonormal set of vectors in Rn and U = (ul, u2, uk) then UTU = Ik (the k k identity matrix).
Speculate sales : Speculate on the projected sales. Justify your product or service by the numbers; discuss your projected revenue gain. Note: it MUST have an ROI that justifies the project for...
8.6 In Figure P8.6 the experimental unit step response of a process system is shown. (a) What is the transfer function that can be used to best describe the system dynamics among the following. 1 (1)...
An 84 year old female arrives to the ER today with her son with a complaint of new onset of confusion. What are your differential diagnoses for a patient with new altered mental status? Go through...

(a) Explain why the incidence matrix for a disconnected graph can be written in block diagonal matrix...

Question:

в о

Step by Step Answer:

a If the first k vertices belong to one component and the ...View the full answer

Applied Linear Algebra

Students also viewed these Linear Algebra questions