Recent content by zohapmkoftid

Homework Statement Show that every m×n matrix A with m linearly independent rows can be obtained from n × n matrix by deleting the last n − m rows. Homework Equations The Attempt at a Solution I have no idea of this question

Yes, it is very easy to prove that. Thanks!

Homework Statement http://uploadpie.com/fHoAj Homework Equations The Attempt at a Solution [PLAIN][PLAIN]http://uploadpie.com/fCgEI

Homework Statement [PLAIN]http://uploadpie.com/nsXSv Homework Equations The Attempt at a Solution I have no idea how to start. To be linearly independent, c1u1+c2u2+...+cnun = 0 has only trivial solution. But I don't know how can I use the given information to prove that

Homework Statement Suppose n > 1 people are positioned in a feld, so that each has a unique nearest neighbour. Suppose further that each person has a ball that is thrown at the nearest neighbour. A survivor is a person that is not hit by a ball. Prove that if n is odd, then there is at least...

Can I prove like this? AB = I det(AB) = detI (detA)(detB) = 1 detA != 0 and detB != 0 Therefore, A-1 and B-1 exist AB = I A-1AB = A-1 B = A-1 BA = A-1A BA = I

ABA = A BAB = B We can conclude that BA = I ?

Could you give me some hints?

The thing confuses me is the definition of inverse B is the inverse of A if AB = BA = I B is the inverse of A if AB = I Which one is the correct definition? ABA = IA A-1ABA = A-1A BA = I

Sorry, I have no clue about this question. I found some solutions on the web but they are related to vector space which I haven't learned yet

Homework Statement Let A and B be n × n matrices. Show that if AB = I, then also BA = I, so A and B are invertible, A = B−1 and B = A−1. How can I prove this? Thanks Homework Equations The Attempt at a Solution

Thanks. I understand now

[PLAIN]http://uploadpie.com/mHyHp Is this correct?

But how can we prove rX0 + sX1 = 0 from A(rX0 + sX1) = 0

Homework Statement The following are two first order logic statements of the statement "There are infinitely many prime numbers" 1. http://uploadpie.com/3PZlO 2. [PLAIN][PLAIN]http://uploadpie.com/PN5i8 Can anyone explain why the second one is wrong? Thanks for help! Homework Equations...