Question: Show that if E is an elementary matrix then ET is an elementary matrix of the same type as E.

Show that if E is an elementary matrix then ET is an elementary matrix of the same type as E.

Step by Step Solution

★★★★★

3.40 Rating (153 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

If E is an elementary matrix of type I or II then E is symmetric ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Document Format (1 attachment)

Word file Icon

949-M-L-A-E (510).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

Find the inverse of each matrix in Exercise 1. For each elementary matrix, verify that its inverse is an elementary matrix of the same type. Exercise 1 (c) 0 1 01 (d) | () 5 0

Q:

The product of two elementary matrices is an elementary matrix. In this case answer true if the statement is always true and false otherwise. In the case of a true statement, explain or prove your...

Q:

Show that if is an elementary matrix, then at least one entry in the third row must be a zero. 00c 3 10

Q:

5 Part 1. Let a be the number of letters in your first name, and let b be the number of letters in your last name. (E.g. If your name is Chen Ning Robert Mills then you would put a = 4, the number of...

Q:

Which of these statements are true?\ If E is an elementary matrix then so is E^(T) .\ If U and V are invertible 7\\\\times 7 matrices then U is row-equivalent to V .\ Any invertible matrix is the...

Q:

Let E be the elementary matrix E 3 of Example 6. Show that EA is the result of interchanging the first two rows of the matrix A. Example 6 Example 6 We obtain some typical elementary matrices as...

Q:

Let E be the elementary matrix E 1 of Example 6. If A is a 2 x 2 matrix, show that EA is the result of multiplying the first row of A by 3. Example 6 Example 6 We obtain some typical elementary...

Q:

Let E be the elementary matrix E 2 of Example 6 and suppose that A is a 3 x 3 matrix. Show that EA is the result upon adding twice the first row of A to its third row. Example 6 Example 6 We obtain...

Q:

5 Part I. Let a be the number of letters in your first name, and let b be the number of letters in your last name. (E.g. If your name is Chen Ning Robert Mills then you would put a = 4, the number of...

Q:

1. For each of the following statements, either prove it or give a counterexample to the statement. [15 marks] (a) If A and D are both invertible n x n matrices then so is ADAT. (b) If A2 = A and A...

Q:

1000 kg dry weight of non porous solid is dried under constant drying conditions with an air velocity of 0.75 m/s, so that the area of drying surface is 55 m. The critical moisture content of the...

Q:

Your former college roommate calls you and asks to borrow $10,000 so the he can open a pizza restaurant in his hometown. He acknowledges that there is a high degree of direct competition in this...

Q:

What theoretically happens to the market price of the share if the company decides to issue a scrip / bonus share to their shareholders? Higher price per share as the total shares will decrease, but...

Q:

Which one of these types is generally not a stakeholder? A. Project Manager B. Sponsor C. Project Observer D. Project Team Member

Q:

Let A be an n n matrix. Prove that the characteristic polynomial of A has degree n. Prove that the coefficient of n in the characteristic polynomial is 1.

Q:

Use the result in Exercise 16 to show that if then the solutions of the characteristic equation of A are Use this result to show that A has (a) Two distinct real eigenvalues if (a - d)2 + 4bc > 0 (b)...

Q:

Prove: If a, b, c, and d are integers such that a + b = c + d, then has integer eigenvalues-namely, λj = a + b and λ2 = a - c. LA

Q:

Please show cell references/formulas. Thank you. Suppose that in January 2006, Kenneth Cole Productions had EPS of $1.65 and a book value of equity of $12.05 per share. Complete the steps below using...

Q:

5. MO Ltd. is considering a five-year project to expand its production efficiency. Building a new plant for $1,000,000 at the beginning of the project is estimated to result in annual sales quantity...

Q:

Emily has borrowed $ 1 0 0 0 0 0 0 from MQ Bank for 1 0 years at an interest rate of j 2 = 4 . 1 % p . a . She will make 1 0 annual repayments. According to the loan agreement, Emily's repayments...