Think of Rn as consisting of rows. If A is m n and AAT is invertible,
Question:
If A is m × n and AAT is invertible, show that E - AT(AAT)-1 A is a projection matrix.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 58% (12 reviews)
If AA T is inverti...View the full answer
Answered By
Fahmin Arakkal
Tutoring and Contributing expert question and answers to teachers and students.
Primarily oversees the Heat and Mass Transfer contents presented on websites and blogs.
Responsible for Creating, Editing, Updating all contents related Chemical Engineering in
latex language
4.40+
8+ Reviews
22+ Question Solved
Related Book For
Question Posted:
Students also viewed these Linear Algebra questions
-
(a) Show that is invertible if and only if a 0 and b 0. (b) If A and B are square and invertible, show that (i) the block matrix Is invertible for any Xi and (ii) (c) if is invertible, show that A...
-
Let A be an m n matrix with linearly independent columns. Explain why ATA must be an invertible matrix. Must AAT also be invertible? Explain.
-
If A is an invertible n à n matrix, show that adj A is also invertible and that (adj A)-1- A = adj (A-1) det A
-
A magnet of mass 5 . 0 1 kg is suspended from the ceiling by a cord as shown. A large magnet is somewhere off to the right, pulling on the small hanging magnet with a constant force of F = 8 0 . 4 N...
-
Multiple Choice Questions The following questions deal with independence of auditors. Choose the best response. a. The operational auditor's independence is most likely to be compromised when the...
-
What are the assumption made for the establishment of Bernoulli's equation?
-
You have completed an audit of activities within the Purchasing Department of Zale Company. The department employs thirty buyers, seven supervisors, a manager, and clerical personnel. Purchases total...
-
Emily Johnson recently joined Growth Chemicals, Inc., as assistant controller. Growth Chemicals processes chemicals for use in fertilizers. During her first month on the job, Emily spent most of her...
-
What particular challenges do students face in online learning environments? Explain some preparation strategies to become a successful online student by detailing at least four steps to manage these...
-
Express the following points in Cartesian coordinates: (a) P(1, 60, 2) (b) Q(2, 90, 4) (c)R(, 45, 210) (d) T(4, /2, /6)
-
If U is a subspace of Rn, show how to find an n n matrix A such that U = [X|AX = 0}.
-
In each case, write X as the sum of a vector in U and a vector in U. (a) X = [2 1 6], U = span{[3 -1 2], [2 0 -3]} (b) X = [2 0 1 6], U = span{[l 1 1 1], [ 1 1 -1 -1], [1 -1 1 -1]} (c) X = [a b c d],...
-
Group spirit improves team decisions. True/False?
-
On its chromosome, an E. coli cell has the genotype lacI lacZ+ lacY+ lacA+. It has an F factor with the genotype lacI+ lacZ+ lacY+ lacA+. What is the expected level of expression of the lac operon...
-
The basal transcription apparatus is composed of a. five general transcription factors. b. RNA polymerase II. c. a DNA sequence containing a TATA box and transcriptional start site. d. all of the...
-
Which of the following base sequences is used during transcription? a. Promoter and terminator b. Start and stop codons c. Ribosome-binding site d. Both a and b
-
A paracentric inversion a. includes the centromere within the inverted region. b. does not include the centromere within the inverted region. c. has two adjacent inverted regions. d. is an inverted...
-
In the triplet-binding assay carried out by Nirenberg and Leder, an RNA triplet composed of three bases was able to cause the a. translation of a polypeptide. b. binding of a tRNA carrying the...
-
Record journal entries for the following transactions of Mason Suppliers. A. Sep. 8: Purchased 50 deluxe hammers at a cost of $95 each from a manufacturer. Credit terms are 5/ 20, n/60, invoice date...
-
What is an insurable interest? Why is it important?
-
The set W of all 2 ( 2 symmetric matrices is a subspace of M22. Find three 2 ( 2 matrices v1, v2, and v3 so that every vector in W can be expressed as a linear combination of v1, v2, and v3.
-
(a) Show that a line t 0 through the origin of R3 is a subspace of R3. (b) Show that a line t in R3 not passing through the origin is not a subspace of R3.
-
The set W of all 2 ( 2 matrices A with trace equal to zero is a subspace of M22. Let Show that span S = W.
-
When Patey Pontoons issued 6 % bonds on January 1 , 2 0 2 4 , with a face amount of $ 6 0 0 , 0 0 0 , the market yield for bonds of similar risk and maturity was 7 % . The bonds mature December 3 1 ,...
-
Accountants distinguish between capital and revenue expenditures for some types of transactions. The entries for such transactions can be made to any one of the following accounts: Balance sheet...
-
The following income statement and balance sheets for Virtual Gaming Systems are provided. VIRTUAL GAMING SYSTEMS Income Statement For the Year Ended December 3 1 , 2 0 2 4 Net sales $ 3 , 0 2 6 , 0...
Study smarter with the SolutionInn App