Let A and B be symmetric n n matrices. Prove that AB = BA if and

Question:

Let A and B be symmetric n × n matrices. Prove that AB = BA if and only if AB is also symmetric.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra with Applications

ISBN: 978-0131857858

7th edition

Authors: Steven J. Leon

See More Books

Question Posted: Jun 13, 2016 12:44 AM

See More Questions

Let A and B be symmetric matrices. (a) Show that A + B is symmetric. (b) Show that AB is symmetric if and only if AB = BA.
Let A and B be symmetric n n matrices and let C = AB. Is C symmetric? Explain.
Let A and B be positive definite symmetric n ( n matrices and let c be a positive scalar. Show that the following matrices are positive definite. (a) cA (b) A2 (c) A + B (d) A-1 (First show that A is...
Consider two polluting firms with cost functions C j (x j ,e j ). The inverse demand function is P(X). Firms engage in negotiations about the permit allocation and a transfer price in a first stage...
Calculate the duration of a $100,000 fixed-rate 30-year mortgage with a nominal annual rate of 7.0%. What is the expected percentage change in value if the required rate drops to 6.5% immediately...
Contrary to some predictions, wholesalers have not died out. What has happened to wholesalers in recent years?
An experiment was conducted to study the effects of temperature $\left({ }^{\circ} \mathrm{C} ight)$ and quantity (g) on the solubility of a chemical in the laboratory. Analyze this experiment....
Given the following data, calculate: (a) BEPx; (b) BEP$; (c) The profit at 100,000 units: P = $8/unit V = $4/unit F = $50,000
Find f'(x) and find the equation of the line tangent to the graph of f at x = 3. f(x)= 5x 2* f'(x)=
Write a program that will take as input two Web page URLs and find a path of links from one to the other. What is an appropriate search strategy is bidirectional search a good idea? Could a search...
Let A be an m n matrix. (a) Explain why the matrix multiplications ATA and AAT are possible. (b) Show that ATA and AAT are both symmetric.
A matrix A is said to be skew-symmetric if AT = -A. Show that if a matrix is skew-symmetric then its diagonal entries must all be 0.
a) Which will be smoother, a 50-day or a 200-day moving average? b) Which will be smoother, a single exponential smoothing (SES) model using = 0.10 or a model using = 0.80? c) What is the...
Clonex Labs, Incorporated, uses the weighted-average method of process costing. The following data are available for one department for October: Percent Completed Work in process, October 1 Work in...
Ultrasound probes can resolve structural details with size approximately equal to the wave length of the ultrasound waves themselves. What is the size of the smallest feature observable in human...
Part 2 Model building Question 1: Company A is a cell phone seller. The company anticipates nationwide demand for the next year to be 20000 units in Nova Scotia, 30000 units in Ontario and 10000...
Restaurant furnishings with an original cost of $38,000 and accumulated depreciation account of $32,000, was sold for $4,200 cash. How will the proceeds of the sale be reported in a SCF, indirect...
What steps does your organization take to ensure ethical marketing practices, particularly in the context of evolving consumer protection regulations and societal expectations?
A company that assembles trucks produces 60 trucks during the current year and incurs $4.5 million of material, labor, and overhead costs. Fifty-three trucks were sold during the year and each is...
What can you do to reduce hunger where you live? To reduce hunger globally?
x + y + z = 5 x + y - 4z = 10 - 4x + y + z = 0 Solve the system by inverting the coefficient matrix and using Theorem 1.6.2.
3x1 + 5x2 = b1 x1 + 2x2 = b2 Solve the system by inverting the coefficient matrix and using Theorem 1.6.2.
Solve the following general system by inverting the coefficient matrix and using Theorem 1.6.2. x1 + 2x2 + 3x3 = b1 x1 - x2 + x3 = b2 x1 + x2 = b3 (a) b1= - 1, b2 = 3, b3 = 4 (b) b1 = - 1, b2 = -1,...
Prob. 1(a). Consider a stock currently trading at $40.25. For a strike price of $38, you want to price both a call and put option that matures 90 days from now. The volatility of the stock (2) is...
Wildhorse sells a snowboard, WhiteOut, that is popular with snowboard enthusiasts. Presented below is information relating to Wildhorse's purchases of WhiteOut snowboards during September. During the...
The following unadjusted trial balance is prepared at fiscal year-end for Nelson Company. Nelson Company uses a perpetual inventory system. It categorizes the following accounts as selling expenses:...

Let A and B be symmetric n n matrices. Prove that AB = BA if and

Question:

Step by Step Answer:

Let A and B be symmetric ...View the full answer

Linear Algebra with Applications

Students also viewed these Linear Algebra questions