Right-multiplication by an elementary matrix E affects the columns of A in the same way that left-multiplication

Question:

Right-multiplication by an elementary matrix E affects the columns of A in the same way that left-multiplication affects the rows. Use Theorems 5 and 3 and the obvious fact that ET is another elementary matrix to show that
det AE = (det E) (det A?

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: 978-0321791542

4th edition

Authors: David C. Lay

See More Books

Question Posted: May 02, 2016 12:02 PM

See More Questions

Predict the result of each multiplication by an elementary reduction matrix, and then check by multiplying it out. (a) (b) (c) (d) (e) 0 1 3 4 () (1 2) 3 4 (12 % 2) 0 13 4 4 3 40 1 120 1 34/(1
In each case find an elementary matrix E such that B = EA. (a) (b) (c) (d) (e) (f) 2 3 -1 2 0 1 1-2 1-43 2 3 2 1 2
Let In each case, find an elementary matrix E that satisfies the given equation. EA = C 2 -1 -1 B = -1 1 C = D = -3 -1 3 2 1 -1 -1 || A/
Can public works increase equilibrium wages?
Suppose the mean clear height of all U.S. Class A warehouses is unknown but the standard deviation is known to be 4 feet.What is the value of the mean clear height if 29% of U.S. Class A warehouses...
Table 118 identifies twenty-six steps in project planning and control. Below is a description of each of the twenty-six steps. Using this information, fill in columns 1 and 2 (column 2 is a group...
What is the most important vibration parameter for monitoring machinery overall health?
On January 1, 2010, Carolinas Corporation had the following stockholders equity accounts. Common stock ($20 par value, 60,000 shares issued and outstanding) ... $1,200,000 Paid-in Capital in Excess...
As you lead your organization's performance management efforts, your chief human resources officer has real concerns about the buy-in among your staff. She has come to you to share her thoughts. With...
The numbers of blocked intrusion attempts on each day during the first two weeks of the month were 56, 47, 49, 37, 38, 60, 50, 43, 43, 59, 50, 56, 54, 58 After the change of firewall settings, the...
Verify that det A = det B + det C, where However, that A is not the same as B + C? a1 a12 A=| a21 a22 v u2 + v2 U) a21 (122 11 21,C a31a32U3 a 12 1 a21 a31 a32V3 Lo
Compute det ATA and det AAT for several random 4 ( 5 matrices and several random 5 ( 6 matrices. What can you say about ATA and AAT when A has more columns than rows?
Derive an expression for the equivalent spring constant when two similar springs are connected: (a) in parallel, (b) in series.
Explain the deterministic safety assessment (DSA) of nuclear reactors and development growth of this methodology over the years.
Review the information in Figure 2.4. Choose a rate of trading cherries for apples different from the rate used in the text (15 pounds of cherries for 10 pounds of apples) that will allow you and...
The spreadsheet in Table 1 provides data on the U.S. economy: Column A is the year; the other columns are quantities sold in millions per year of compact discs (column B), music videos (column C),...
Return to Table 7.12. In the top half of the table, at what point does diminishing marginal productivity kick in? What about in the bottom half of the table? How do you explain this? Table 7.12...
In June 2014, the international price of crude oil was about \$114 per barrel (Brent benchmark). Three years later, it was about $\$ 47$ per barrel. This dramatic price reduction caused petroleum...
The chief accountant of Shirts Galore Ltd believes that the entitys yearly allowance for doubtful debts should be 2% of net credit sales. The managing director of Shirts Galore Ltd, nervous that the...
What is the difference between the straight-line method of depreciation and the written down value method? Which method is more appropriate for reporting earnings?
Let where a, b, and c are positive (for simplicity). Compute the area of the parallelogram determined by u, v, u + v, and 0, and compute the determinants of the matrices [u v] and [v u]. Draw a...
A is an n x n matrix. Mark each statement True or False (T/F). Justify each answer. (T/F) An n x n determinant is defined by determinants of (n -1) (n -1) submatrices.
Justify each answer (T/F) Cramers rule can only be used for invertible matrices.
Compare and contrast different deadlock prevention techniques such as resource ordering, the "hold and wait" condition, and preemptive resource allocation. Which methods are most effective for...
The following information is taken from Aden Company's records: Product Group Units Cost/Unit Market/Unit A 1 700 $1.10 $0.90 B 1 250 1.50 1.55 C 2 150 4.90 5.15 D 2 100 6.50 6.40 E 3 80 25.00 24.60...
American Food Services, Incorporated leased a packaging machine from Barton and Barton Corporation. Barton and Barton completed construction of the machine on January 1, 2024. The lease agreement for...

Right-multiplication by an elementary matrix E affects the columns of A in the same way that left-multiplication

Question:

Step by Step Answer:

By Theorem 5 det AE det AE T Since AE T E T A T det A...View the full answer

Linear Algebra and Its Applications

Students also viewed these Linear Algebra questions