# Some linear algebra problems i need help with

#### skybluekitty

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

Related Calculus and Beyond Homework Help News on Phys.org

#### woox

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