Let A be any n xn matrix. Prove that the dot product identity v (Aw) =

Question:

Let A be any n xn matrix. Prove that the dot product identity v • (Aw) = (ATv) • w is valid for any vectors v, w ∈ Rn.

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

Let A be an n n matrix. Prove that the following statements are equivalent. (a) N(A) = {0}. (b) A is nonsingular. (c) For each b Rn, the system Ax = b has a unique solution.
Let A be an m x n matrix with rank A = n. (a) Prove that the matrix P = A(ATA)~l AT is a projection matrix, meaning that P2 = P, cf. Exercise 2.5.8. (b) Construct the projection matrix corresponding...
Let .x1.......xn be distinct real numbers. Prove that the n Ã n matrix K with entries
for a manufacturing company product costs include all of the following except direct material overhead costs research and development costs direct labor costs
Copyrights provide authors with a monopoly. (a) What effect would eliminating copyrights have on the price and output of textbooks? (b) Should copyrights be eliminated? (c) Give some other examples...
On June 1, 2020, the City of Cape May authorized the construction of a police station at an expected cost of $250,000. Financing will be provided through transfers from a Special Revenue Fund. The...
Axial dispersion in channel flow. Consider the pressure-driven laminar flow in a channel of height $2 h$. Derive the following formula for the axial dispersion coefficient: \[D_{\mathrm{E}}=\frac{2...
How does deferred or unearned revenue arise? Why can it be classified properly as a current liability? Give several examples of business activities that result in unearned revenues.
The adjusted trial balance for Blossom's Animations is presented below. BLOSSOM'S ANIMATIONS Adjusted Trial Balance December 31, 2024 Debit Credit Cash $3,300 Accounts receivable 4,700 Prepaid...
Bill has just completed his exams for the academic year and wants to celebrate by seeing every movie showing in theaters in his town and in six other neighboring cities. If he travels to another...
Suppose u. v satisfy ||u|| = 3, ||u + v|| = 4. and ||u - v|| = 6. What must ||v|| equal? Does your answer depend upon which norm is being used?
Prove that A = AT is a symmetric n x n matrix if and only if {A v) w = v (A w) for all v. w Rn.
D&B Ice Cream budgeted sales of 136,000 units of flavor C, assuming that the company would have 16 percent of 850,000 units sold in a particular market. The actual results were 126,000 units, based...
Pacific Cruises provides standard riverboat cruises for tourists on the Hawkesbury River. The average cruise has 90 passengers on board. Each passenger pays $100 for a days cruising. The riverboat...
What framework concept works best? Mary uses a March sales report to ponder what the April sales will be. However, a change was made in how sales data is collected from the March period.
Calculate the remaining open to buy balance. February BOM $1,060 February Sales $550 February MDs $248 February receipts on order $875 March BOM $1,340 Feb BOM Feb Sales Feb MD March BOM Mar OTB Feb...
Jerry Silverman owns a local bagel shop. Total sales for his target market are $1.5 million per year. He currently attracts 12 percent of the market. If he increases market share to 18 percent, by...
1. The table on the right shows the most current government economic indicators. How much did the average living standards increase in the US in 2015. Year GDP in billions of current dollars Real...
GSS 2014 respondents were asked to rate their agreement to the statement, Immigrants were good for America. Results are provided in the table below for the percentage in each category by political...
On October 1, 2021, Adoll Company acquired 2,600 shares of its $1 par value stock for $38 per share and held these shares in treasury. On March 1, 2023, Adoll resold all the treasury shares for $34...
For each of your solutions in Exercise 1: (a) Determine the projection p = A. (b) Calculate the residual r(). (c) Verify that r() N(AT).
Find the best least squares fit to the data in Exercise 5 by a quadratic polynomial. Plot the points x = -1, 0, 1, 2 for your function and sketch the graph.
Given a collection of points (x1, y1). (x2 > y2),. . . . . . . . , (xn, yn)> let and let y = c0 + c1x be the linear function that gives the best least squares fit to the points. Show that if = 0 then...
Textile Crafts Company (TCC) sells craft kits and supplies to retail outlets and through online sites such as Etsy.com. Some of the items are manufactured by TCC, while others are purchased for...
Find the missing value in the following table. The following financial statement information is from five separate companies. Company Company Company Company Company A B C D E December 31, 2016...
Sunshine Sushi, a Japanese restaurant, has the following adjusted trial balance with accounts listed in alphabetical order. For the bank loan, $60,550 is due in 2024. For Notes receivable, $41,500...

Let A be any n xn matrix. Prove that the dot product identity v (Aw) =

Question:

Step by Step Answer:

Using 32 ...View the full answer

Applied Linear Algebra

Students also viewed these Linear Algebra questions