Question

# n×n-matrix M is symmetric if M = M^t. Matrix M is anti-symmetric if M^t = -M....

n×n-matrix M is symmetric if M = M^t. Matrix M is anti-symmetric if M^t = -M.

1. Show that the diagonal of an anti-symmetric matrix are zero

2. suppose that A,B are symmetric n × n-matrices. Prove that AB is symmetric if AB = BA.

3. Let A be any n×n-matrix. Prove that A+A^t is symmetric and A - A^t antisymmetric.

4. Prove that every n × n-matrix can be written as the sum of a symmetric and anti-symmetric matrix.

#### Earn Coins

Coins can be redeemed for fabulous gifts.

##### Need Online Homework Help?

Most questions answered within 1 hours.

##### Active Questions
• A sample is obtained from a population with u=40 and o=6. Which of the following sample...
asked 6 minutes ago
• In a survey, 11 people were asked how much they spent on their child's last birthday...
asked 24 minutes ago
• Discussion 7.1: Practice Critical Thinking How well do you understand this material? Reading the material is...
asked 25 minutes ago
• A credit score measures a​ person's creditworthiness. Assume the average credit score for Americans is 709....
asked 28 minutes ago
• A Database Administrator (DBA) is play both managerial role and technical role in a modern organization;...
asked 43 minutes ago
• The Federal Election Commission collects information about campaign contributions and disbursements for candidates and political committees...
asked 43 minutes ago
• In the week before and the week after a​ holiday, there were 10,000 total​ deaths, and...
asked 46 minutes ago
• 1. Identify the vertex of the quadratic equation y=2x2+8x-10. using the formula 2. Write the equation...
asked 1 hour ago
• How well do you understand this material? Reading the material is separate than understanding it; further,...
asked 1 hour ago
• Analyze the behavior of capacitors under steady state direct current and high frequency AC current (500...
asked 1 hour ago
• Traffic on the eastbound approach of a signalized intersection is traveling at 48 km/h, with a...
asked 1 hour ago
• Students in a chemistry class convince their teacher to use the following "group grading" scenario. Students...
asked 1 hour ago