-2 3 1. Let A 5 14 3 32 = such that B A into B)...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
-2 3 1. Let A 5 14 3 32 = such that B A into B) 2. Let A = = and B = ( 3 3 2 1-2 3 Find three elementary matrices E1, E2, and E -5 -1 E3E2E1A. (Hint: notice that three elementary row operations are used to transform ( 2 ). 1 (a) Show that the Reduced Row Echelon Form of A is the identity matrix I2. (b) Find every elementary matrix corresponding to each of the elementary row operation used in (a). (c) Use the result in (a) and (b) to write the inverse of A as a product of elementary matrices. 3. Use the Gauss-Jordan method to find the inverse of A 05 -2 4 12-10 -3 4-1 5 5 " if it exists. 1 0 4. Let A 3 1 2 2 -3 2 (a) Use the Gauss-Jordan method to find A-. (b) Use the result in (a) to solve the linear system (c) Find the inverse of the linear map T(x, y, z) = (x x- z = 0 -3x+y+2z = -3 2x - - 3y+2z = 1 z, -3x+y+2z, 2x 3y+2z). 5. Let T(x, y, z) = (x y + 2z, y 3z) and G(a, b) = (3a + b, a b, a 2b) - (a) Find (TG)(a, b). - (b) Find (GT)(x, y, z). -2 3 1. Let A 5 14 3 32 = such that B A into B) 2. Let A = = and B = ( 3 3 2 1-2 3 Find three elementary matrices E1, E2, and E -5 -1 E3E2E1A. (Hint: notice that three elementary row operations are used to transform ( 2 ). 1 (a) Show that the Reduced Row Echelon Form of A is the identity matrix I2. (b) Find every elementary matrix corresponding to each of the elementary row operation used in (a). (c) Use the result in (a) and (b) to write the inverse of A as a product of elementary matrices. 3. Use the Gauss-Jordan method to find the inverse of A 05 -2 4 12-10 -3 4-1 5 5 " if it exists. 1 0 4. Let A 3 1 2 2 -3 2 (a) Use the Gauss-Jordan method to find A-. (b) Use the result in (a) to solve the linear system (c) Find the inverse of the linear map T(x, y, z) = (x x- z = 0 -3x+y+2z = -3 2x - - 3y+2z = 1 z, -3x+y+2z, 2x 3y+2z). 5. Let T(x, y, z) = (x y + 2z, y 3z) and G(a, b) = (3a + b, a b, a 2b) - (a) Find (TG)(a, b). - (b) Find (GT)(x, y, z).
Expert Answer:
Related Book For
Elementary Linear Algebra with Applications
ISBN: 978-0471669593
9th edition
Authors: Howard Anton, Chris Rorres
Posted Date:
Students also viewed these mathematics questions
-
Analysis of a binary option trading website. a) In a one-step model with risky asset prices \(S_{0}, S_{1}\) at times \(t=0\) and \(t=1\), compute the price at time \(t=0\) of the binary call option...
-
You decided to short 150 shares of AMZN when it was trading at $250 a share. Suppose that your initial margin is 50%. While you are short the stock, AMZN pays a dividend of $6.50 a share. At the end...
-
For your initial post, describe the ways a manager in an organization might want to use persuasion as opposed to a direct request when communicating with employees. In that situation, provide...
-
1. If an industry is formed by six companies. Four companies have sales of $ 10 each, and two companies have sales of $ 5 each. a. What is the concentration ratio of four companies for this industry?...
-
Suppose that {v1, v2, vn} is a linearly independent set of vectors in Rn. Show that if A is an n ( n non-singular matrix, then {Av1, Av2, Ayn} is linearly independent.
-
From the following, prepare a schedule of accounts receivable for AVE Co. for May 31, 2023: Accounts Receivable Subsidiary Ledger Bliss Co. 5/12 SJ1 50 5/25 CRJ1 20 Rowe Co. 5/18 SJ1 60 Partial...
-
Melissa Khan alleges that on May 27, 2004, she entered into a lease and warranty agreement with Riverbank Motors Corporation, Inc. (the Dealership), for a new, 2004 Volkswagen Toureg (the Vehicle),...
-
The comparative balance sheet of Wedge Industries Inc. for December 31, 2014 and 2013 is as follows: The following additional information is taken from the records: 1. Land was sold for $100. 2....
-
Analyses at least two considerations that would be required to ensure effective transaction transparency of centralized database management systems and distributed database management systems....
-
Roberta Santos, age 41, is single and lives at 120 San-borne Avenue, Springfield, IL 60781. Her Social Security number is 123-45-6789. Roberta has been divorced from her former husband, Wayne, for...
-
Suppose you could correctly predict that the business cycle was approaching a trough. What should your investment strategy for stocks be?
-
The induced magnetic field at radial distance 8.1 mm from the central axis of a circular parallel-plate capacitor is 2.2 x 106 T. The plates have radius 4.1 mm. At what rate is the magnitude of the...
-
A form of business organization that is easy to start up and requires no legal registration or paper work. You are in charge of the decisions. All income and expenses from the business activity flow...
-
Jimmy invests $15,000 in an account that pays 6.07% compounded quarterly. How long (in years and months) will it take for his investment to reach $22,000? years and months (Round the answer for...
-
Do you think organizations that promote professional ethics are effective? Why or why not? 2. What should employees do when one of their colleagues or a company executive is being investi-gated for...
-
Contrast current youth unemployment in relation to the following: i. Economic and development planning ii. Market failure iii. Resource misallocation iv. Economic growth models v. Government failure...
-
The Roanoke Shootings On August 26, 2015, two reporters for a Roanoke, Virginia TV station were shot and killed by a former employee while conducting an on-air interview as part of their job. Go to...
-
Why is the national security argument for tariffs questionable?
-
Let \(X_{1}, \ldots, X_{n}\) be a set of independent and identically distributed random variables from a distribution \(F\) with variance \(\mu_{2}\) where \(E\left(\left|X_{1}ight|^{4}ight) a. Prove...
-
Consider a sequence of independent random variables \(\left\{X_{n}ight\}_{n=1}^{\infty}\) where \(X_{n}\) has probability distribution function \[f_{n}(x)= \begin{cases}2^{-(n+1)} &...
-
Let \(X_{1}, \ldots, X_{n}\) be a set of independent and identically distributed random variables from a shifted exponential density of the form \[f(x)= \begin{cases}\exp [-(x-\theta)] & \text { for...
Study smarter with the SolutionInn App