• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Some linear algebra problems i need help with

Let A and B be nxn matrices.
1. Suppose that AB=AC and det A does not equal 0. Show that B=C

2. Show that A is nonsingular if and only if A transpose is nonsingular.

3. Show that det AB = det BA.

4. Show that det AB = 0 if and only if det A=0 or det B=0

5. Show that if AB= -BA and n is odd, then A or B is singular.

6. Show that det A*Atranspose is greater than equal to 0

7. Show that det A*Btranspose = det Atranspose* det B

8. Let A be nxn skew-symmetric matrix. If n is odd, show that det A=0

9. Show that 3x3 vandermonde matrix has a determinant equal to (a-b)(b-c)(c-a) The matrix is
[1 1 1
a b c
a^2 b^2 c^2]
Thank you.

1. Homework Statement

2. Homework Equations

3. The Attempt at a Solution
No one is going to give you the answer without any work. Do your own homework and ask for help here if you need it

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving