Explain why an equation Ax = b has a solution if and only if b is orthogonal

Question:

Explain why an equation Ax = b has a solution if and only if b is orthogonal to all solutions of the equation A^Tx = 0.

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

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra And Its Applications

ISBN: 9781292351216

6th Global Edition

Authors: David Lay, Steven Lay, Judi McDonald

See More Books

Question Posted: May 15, 2023 06:37 AM

See More Questions

Show that if A = A T is a symmetric matrix, then Ax = b has a solution if and only if b is orthogonal to ker A.
(a) Show that AX = B has a solution if and only if rank A = rank[A B]. (b) lf [AX] = B has no solution, show that rank[A B] = 1 + rank A
Mark each statement True or False. Justify each answer. (If true, cite appropriate facts or theorems. If false, explain why or give a counterexample that shows why the statement is not true in every...
Question 2: Consider the market for Florida oranges. The demand for Florida oranges is given by the inverse demand function p = 70-2Q The market cost function for firms that sell Florida oranges is...
The Steelcase Workplace Index studied the types of work-related activities that Americans did while on vacation in the summer. Among other things, 40% read work-related material. Thirty-four percent...
3. Jamie has an undergraduate degree in finance and is employed full-time by a bank. She is taking courses at a local university leading to an MBA degree. a. Is the full cost of this education...
Give examples of relationships that could be tested with chi square and ANOVA.
Determine the error for each of the following forecasts. Compute MAD andMSE. Period Vale Forecast Error 202 191 173 169 202 192 181 174 172 174 179 189 198 211 4 175 182 196 204 219 227 10
Measures of liquidity, Solvency and Profitability The comparative financial statements of Marshall Inc. are as follows. The market price of Marshall Inc. common stock was $ 53 on December 31, 20Y2....
1. Weighted average and first-in, first-out (FIFO) equivalent units would be the same in a period when which of the following occurs? a. No beginning inventory exists. b. No ending inventory exists....
Use the steps below to prove the following relations among the four fundamental subspaces determined by an m x n matrix A. Row A = (Nul A) Col A = .NulA T )? a. Show that Row A is contained in (Nul...
All vectors are in R n . Justify each answer. (T/F) An orthogonal matrix is invertible.
You want to make a major purchase that will involve a large amount of cash and/or credit. What questions will you ask yourself before making such a commitment? Why is it important to make rational,...
Alec is an employee who drives a 2021 Ford C-Max with a fair-market value of $32,000. He has been given the choice to have the fringe benefit reported on his W-2 either using the lease-value rule or...
What resource do most thinking and learning technologies rely on to be effective? a) data b) images c) gas d) robots
Financial Reporting Problem Marks and Spencer plc (M&S) The financial statements of M&S (GBR) are presented in Appendix A. The companys complete annual report, including the notes to the...
Totally Chemical is considering an investment decision project in which the organization expands into the trucking business. Totally Chemical wants to begin this investment decision project by buying...
Presented below is the balance sheet of Sandhill Corporation as of December 31, 2017. SANDHILL CORPORATION BALANCE SHEET DECEMBER 31, 2017 Goodwill (Note 2) Buildings (Note 1) Inventory Land Accounts...
Discretionary fiscal policy is the purview of a. Congress only. b. The president only. c. Congress and the president collectively through law. d. The Federal Reserve.
Fill in each blank so that the resulting statement is true. A solution to a system of linear equations in two variables is an ordered pair that__________ .
Clearly describe what, if anything, is incorrect about each of the following hypotheses. a. H 0 : p 1 p 2 = 0 versus H a : p 1 p 2 0 b. H 0 : = 40 versus H a : < 30 c. H 0 : 1 2 = 0 versus H...
For each of the following studies, indicate whether the data were collected in a paired manner and therefore require a paired analysis. a. A farmer wants to know whether hand-milking or...
Some smoke alarms for homes with children now use a recording of the mothers voice calling the child by name, as opposed to the beeping sound of conventional smoke alarms. a. Describe how you could...
question 6 Timely Inc. produces luxury bags. The budgeted sales and production for the next three months are as follows july. august september Sales, in units 1,115. 1229. 1302 Production. in units...
On May 12 Zimmer Corporation placed in service equipment (seven-year property) with a basis of $220,000. This was Zimmer's only asset acquired during the year. Calculate the maximum depreciation...
Power Manufacturing has equipment that it purchased 7 years ago for $2,550,000. The equipment was used for a project that was intended to last for 9 years and was being depreciated over the life of...

Explain why an equation Ax = b has a solution if and only if b is orthogonal

Question:

Step by Step Answer:

If the equation ...View the full answer

Linear Algebra And Its Applications

Students also viewed these Mathematics questions