Let A be an m x n matrix Suppose that is a (m k) x n matrix whose first m rows are the same as A Prove that kerC ker A Thus, appending more rows cannot increase the size of a matrix 's kernel Give an example where kerC ker A (2)...

Let r 1 r mk be the rows of C so r 1 r m are ...

Let A be an m x n matrix. Suppose that is a (m + k) x n

Question:

Let A be an m x n matrix. Suppose that

is a (m + k) x n matrix whose first m rows are the same as A. Prove that kerC Š† ker A. Thus, appending more rows cannot increase the size of a matrix's kernel. Give an example where kerC ‰ ker A

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 08:33 AM

See More Questions

Let A be an m x n matrix. Show that (a) If x N(ATA), then Ax is in both R(A) and N(AT). (b) N(ATA) = N(A). (c) A and ATA have the same rank. (d) If A has linearly independent columns, then ATA is...
Let A be an m x n matrix, B an n x r matrix, and C = AB. Show that (a) N(B) is a subspace of N(C). (b) N(C)- is a subspace of N(B) and, consequently, R(CT) is a subspace of R(BT).
Let A be an m x n matrix of rank r and let |x1,..., xr} be a basis for R(AT). Show that {Ax1,. . . .. . ., Axr] is a basis for R(A).
What is the present value of $9,000 received: a. Twenty eight years from today when the interest rate is 10% per year? b. Fourteen years from today when the interest rate is 10% per year? c. Seven...
Describe giving reasons, organizational structure that would be most appropriate in each of the following cases 1. A small manufacturing company operating from a single site employing about 50 people...
Distinguish between different costing systems. LO1
8.4 8
Customers call a call center to make room reservations for a small chain of 42 motels located throughout the southwestern part of the United States. Business analytics is used to determine how and if...
Exercise 8-12 a-b Elburn Supply Co. has the following transactions related to notes receivable during the last 2 months of 2020. The company does not make entries to accrue interest except at...
Jimmy owns a garden in which he has planted N trees in a row. After a few years, the trees have grown up and now they have different heights. Jimmy pays much attention to the aesthetics of his...
Characterize the range and kernel of the following matrices: (a) (b) (c) (d) 8 4 -6 3 12 3-5 2 124 0113 1022
Let A be an m n matrix. Suppose that C = (A B ) is an m (n + k) matrix whose first n columns are the same as A. Prove that mgC mg A. Thus, appending more columns cannot decrease the size of a...
Completing T-Accounts For each transaction in M2-5 (including the sample), post the effects to the appropriate T-accounts and determine ending account balances. Beginning balances areprovided. Cash...
Why the sudden increase in income before taxes in 2021? 8. Why were the operating assets the highest in 2019? 9. Why are the short-term loans the highest in 2020? 10. Why are the other long-term...
Mercy wants to make sure that she will be able to provide for her daughter's college and plans to open a savings account with a bank that is ready to pay interest as shown below per year compounded...
Question 1. For a firm that uses portfolio management, please give a real or hypothetical example of how the CEO's personal bases for power help organizational performance. Question 2. Give a real...
Make a schedule that you would use that effectively illustrates working with paraprofessionals that includes collaboration time. Use the examples provided in the following resources to guide your...
How does the integration of technology and automation influence employee motivation and job satisfaction within modern organizational contexts ?
Briefly define each term. a. Coordination number b. Ligand c. Bidentate and polydentate d. Complex ion e. Chelating agent
XYZ Inc. a calendar year, accrual basis corporation, had the following items during 2021: Gross revenue from operations Cost of goods sold $420,000 ($180,000) $9,000 LT capital gain .LT capital...
Let V denote the set of positive real numbers. Define the operation of scalar multiplication, denoted , by x = x for each x R+ and for any real number a. Define the operation of addition, denoted...
Let Z denote the set of all integers with addition defined in the usual way and define the scalar multiplication, denoted , by a k = [[]] k for all k Z where [[]] denotes the greatest integer less...
Let S denote the set of all infinite sequences of real numbers with scalar multiplication and addition defined by {an} = {an} {an} + {bn} = {an + bn} Show that 5 is a vector space.
Milano Pizza is a small neighborhood pizzeria that has a small area for in-store dining as well as offering take-out and free home delivery services. The pizzerias owner has determined that the shop...
Which of the following statement regarding a post-closing trial balance is not true
What are the benefits and potential risks factors for undertaking derivative strategies compared to cash transactions

Let A be an m x n matrix. Suppose that is a (m + k) x n

Question:

с-(2)

Step by Step Answer:

Let r 1 r mk be the rows of C so r 1 r m are ...View the full answer

Applied Linear Algebra

Students also viewed these Linear Algebra questions