Suppose A is an n x n matrix with the property that the equation Ax = b
Question:
Suppose A is an n x n matrix with the property that the equation Ax = b has at least one solution for each b in Rn.
Without using Theorems 5 or 8, explain why each equation
Ax = b has in fact exactly one solution.
Data from in Theorem 5
Data from in Theorem 8
Transcribed Image Text:
If A is an invertible n × n matrix, then for each b in R", the equation Ax = b has the unique solution x = A-¹b.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 75% (8 reviews)
Since the equation Ax b has a solution for each b the matrix A has a pivot in ...View the full answer
Answered By
Munir Ahmed Jakhro
I am professional Tutor of of Business Courses, I did my four years Bachelor Degree from one of the Top Business schools of World "Institute of Business Administration" in year 2013. Since then I have been working as Tutor of Accounting, Finance tutor on different online platforms like this website. I am have experience of 6 years teaching business courses to students online and offline my professional job at national savings also helped me in accounting understanding .
4.90+
8+ Reviews
10+ Question Solved
Related Book For
Linear Algebra And Its Applications
ISBN: 9781292351216
6th Global Edition
Authors: David Lay, Steven Lay, Judi McDonald
Question Posted:
Students also viewed these Mathematics questions
-
Suppose A is an m ( n matrix with the property that for all b in the equation Ax = b has at most one solution. Use the definition of linear independence to explain why the columns of A must be...
-
Suppose A is an n x n matrix with the property that the equation Ax = 0 has only the trivial solution. Without using the Invertible Matrix Theorem, explain directly why the equation Ax = b must have...
-
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...
-
Products are 1. Lip gloss or lipstick with SPF 2. Custom facial sheets you can make online or in store pickup and have it send to your home based on your needs 3. A foundation sunscreen Price Provide...
-
Using the data given in E8-17, calculate the following overhead variances: a. Spending variance. b. Production-volume variance. c. Efficiency variance. d. Was the factory overhead under- or over...
-
Maller Manufacturing Company makes two different products, M and N. The company's two departments are named after the products; for example, Product M is made in Department M. Maller's accountant has...
-
Prepare a list of possible objections to the products, and your responses to them.
-
The Olde Town Microbrewery makes Townside beer, which it bottles and sells in its adjoining restaurant and by the case. It costs $1700 to set up, brew, and bottle a batch of the beer. The annual cost...
-
Oriole Railroad Co. is about to issue $260,000 of 10-year bonds paying an 10% interest rate, with interest payable annually. The discount rate for such securities is 8%. Click here to view the factor...
-
Imagine that Howard has asked you to write some queries to help him make better use of his data. For each information request below, write a single query that provides the answer set. When a task...
-
T is a linear transformation from R into R. Show that T is invertible and find a formula for T -1 . T(x, x) = (-9x +7x2, 4x - 3x2)
-
Let T be a linear transformation that maps R n onto R n . Show that T - exists and maps R n onto R n . Is T - also one-to- one?
-
Edge Company produces two models of its product with the same machine. The machine has a capacity of 176 hours per month. The following information is available. Required 1. Determine the...
-
When listing the possible values of the hypergeometric random variable X, it must be the case that x is less than or equal to the smaller of n or k. Why?
-
Explain the similarities and differences between the hypergeometric probability distribution and the binomial probability distribution.
-
Study the following and answer the questions below. The trial balance of Mary Harris (Gowns) as at 31 December 2015 showed a difference which was posted to a suspense account. Draft final accounts...
-
What criteria must be satisfied for a random variable X to be a hypergeometric random variable?
-
Determine whether the probability experiment represents a binomial experiment. If not, explain why. (a) An urn contains 20 colored golf balls: 8 white, 6 red, 4 blue, and 2 yellow. A child is allowed...
-
Suppose the government decides to reduce taxes today by 1% of GDP, financed by higher borrowing, with the borrowing to be repaid 10 years from now with higher taxes. Discuss the various arguments...
-
Will the prediction interval always be wider than the estimation interval for the same value of the independent variable? Briefly explain.
-
How large a sample would be needed to ensure that the length of the CI in Problem 6.30 is 0.5 g/mL assuming the sample standard deviation remains at 2.0 g/mL? Pharmacology Suppose we want to estimate...
-
What is the best estimate of the 1971 incidence rate from these data? Environmental Health Much discussion has taken place concerning possible health hazards from exposure to anesthetic gases. In one...
-
Provide a 95% CI for the true incidence rate? Environmental Health Much discussion has taken place concerning possible health hazards from exposure to anesthetic gases. In one study conducted in...
-
Write an interactive java application where you create two arrays - one String array where you store the name of your monthly bills (viz. Grocery, Utility, Phone, Electricity, Internet etc) and one...
-
5. A 72.0 cm long stretched string is resonating at the third harmonic. If the source frequency is 460 Hz, then what is the speed of the wave? Answer in m/s.
-
-20- N16/4/PHYSI/HP3/ENG/TZ0/XX (Option B continued) .12. The diagram shows two methods of pedalling a bicycle using a force F. Method 1 crank arm Method 2 crank arm [2] 121 In method 1 the pedal is...
Study smarter with the SolutionInn App