Let R be a row-echelon form of an invertible n n matrix. Show that solving the

Question:

Let R be a row-echelon form of an invertible n × n matrix. Show that solving the linear system Rx = b by back-substitution requires
n2/2 - n/2 multiplications and n2/2 - n/2 additions

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

Step by Step Answer:

Related Book For book-img-for-question

Elementary Linear Algebra with Applications

ISBN: 978-0471669593

9th edition

Authors: Howard Anton, Chris Rorres

See More Books

Question Posted: Jun 17, 2016 08:14 AM

See More Questions

Find a row echelon form of each of the given matrices. Record the row operations you perform, using the notation for elementary row operations. (a) (b) A=1-3 4 1 1 10 4 -6 -4 -2-14 4 2 113 124
Let A be a nonsingular n n matrix and let B be an n r matrix. Show that the reduced row echelon form of (A|B) is (I|C), where C = A-1B.
If the row echelon form of A involves free variables, then the system Ax = b will have infinitely many solutions. In this case answer true if the statement is always true and false otherwise. In the...
Suppose a single 802.11n client is connected to an 802.11n access point and there is no other client or access point in the neighborhood. The client senses the medium, then sends a 2000-Byte frame,...
Which countries appear to have benefited the most from international trade during the last few decades? What policies do these countries seem to have in common? Does their experience lend support for...
What is the general rule for valuing an asset received in exchange for a dissimilar asset and cash?
In starting to set a final price: 1 List two pricing objectives and three pricing constraints. 2 Think about your customers and competitors and set three possible prices. 3 Assume a fixed cost and...
Qtip Corp. owns stock in Maxey Corp. The investment represents a 10 percent interest, and Qtip is unable to exercise significant influence over Maxey. The Maxey stock was purchased by Qtip on January...
Supposed a top fortune 500 company is selling a 30-year bond with a semiannual coupon of 12 percent, when the going rate on such a bond is 8 percent. How much would you be willing to pay for this...
Mercer Asbestos Removal Company removes potentially toxic asbestos insulation and related products from buildings. There has been a long-simmering dispute between the companys estimator and the work...
Derive the formula l2 + 22 + 32 + ... + n2 = n(n + 1) (2n +1)/6 Using the following steps. (a) Show that (k + l)3 - k3 = 3k2 + 3k + 1. (b) Show that [23 - 13] + [33 - 23] + [43 - 33] + ... + [(n +...
Use the method of Example 1 and the LU-decomposition To solve the system 3x1 - 6x2 = 0 -2x1 + 5x2 = 1 2 1 2 2 2
Beginning three months from now, you want to be able to withdraw $2,500 each quarter from your bank account to cover college expenses over the next 4 years. If the account pays .47 percent interest...
Based on the case, Insights Analytics: Technology for a Knowledge Management Program attached . Please explain all 8 points. Explanation of each point should be 300words . Please attach the reference...
When women were finally allowed to become pilots of fighter jets, engineers needed to redesign the ejection seats because they had been originally designed for men only. The ejection seats were...
What will be the output of the following code snippet? with open ("hello.txt", "w") as f: f.write("Hello World how are you today") with open('hello.txt', 'r') as f: data = f.readlines () for line in...
Assume that females have pulse rates that are normally distributed with a mean of p = 72.0 beats per minute and a standard deviation of o = 12.5 beats per minute. Complete parts (a) through (c)...
The proposed rates were not in the range the CEO expected given the pricing analysis. The CEO has asked the pricing actuary to verify the total projected loss cost excluding potential large storm...
For the half-cell reaction ClO 4 - (aq) + 8 H + (aq) + 7 e - 1 / 2 Cl 2 (g) + 4 H 2 O(l), what are the standard-state conditions for the reactants and products?
Draw a Feynman diagram for the reaction n + v p + .
Let A Rmn, B Rnr, and let x, y Rn. Suppose that the product AxyTB is computed in the following ways: (i) (A(xyT))B (ii) (Ax)(yTB) (iii) ((Ax)yT)B (a) How many scalar additions and multiplications...
Let Eki be the elementary matrix formed by subtracting a times the ith row of the identity matrix from the kth row. (a) Show that Eki = 1 - aekeTi. (b) Let Eji = I - ejeTi. Show that EjiEki = I - (ek...
Let A be an n n matrix with triangular factorization LU. Show that det(A) = u11u22 unn
Which of the following are elements of a bootstrappable business model? Indicate ALL that apply. Large up-front capital investment Recurring revenue stream Long sales cycles Word of mouth advertising
Hooligan Adventure Supply produces and sells various outdoor equipment. The Molding and Assembly production departments are supported by the Personnel and Maintenance departments. Personnel costs are...
Kelley Enterprises In October 1989, Pat Kelley.wus in his office, preparing the 1990 budget and contemplating the recent races of his business. Orders had been plentiful Lately that he though that...

Let R be a row-echelon form of an invertible n n matrix. Show that solving the

Question:

Step by Step Answer:

Since R is a rowechelon form of an invertible n n matrix it has ones ...View the full answer

Elementary Linear Algebra with Applications

Students also viewed these Linear Algebra questions