Question

Problem 30. Show that if two matrices A and B of the same size have the...

Problem 30. Show that if two matrices A and B of the same size have the property that Ab = Bb for every column vector b of the correct size for multiplication, then A = B.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let matrices A,B∈Mn×n(R). Show that if A and B are each similar to some diagonal matrix,...
Let matrices A,B∈Mn×n(R). Show that if A and B are each similar to some diagonal matrix, and also have the same eigenvectors (but not necessarily the same eigenvalues), then  AB=BA.
If A and B are matrices, A has size m × n, and the multiplication ABA...
If A and B are matrices, A has size m × n, and the multiplication ABA is defined, what can you say about the size of B, if anything?
If A and B are matrices and the columns of AB are independent, show that the...
If A and B are matrices and the columns of AB are independent, show that the columns of B are independent.
Show that the product of two n × n unitary matrices is unitary. Is the same...
Show that the product of two n × n unitary matrices is unitary. Is the same true of the sum of two n × n unitary matrices? Prove or find a counterexample.
We say two n × n matrices A and B are similar if there is an...
We say two n × n matrices A and B are similar if there is an invertible n × n matrix P such that A = PBP^ -1. a) Show that if A and B are similar n × n matrices, then they must have the same determinant. b) Show that if A and B are similar n × n matrices, then they must have the same eigenvalues. c) Give an example to show that A and B can be...
Prove the following statements: a) If A and B are two positive semidefinite matrices in IR...
Prove the following statements: a) If A and B are two positive semidefinite matrices in IR ^ n × n , then trace (AB) ≥ 0. If, in addition, trace (AB) = 0, then AB = BA =0 b) Let A and B be two (different) n × n real matrices such that R(A) = R(B), where R(·) denotes the range of a matrix. (1) Show that R(A + B) is a subspace of R(A). (2) Is it always true...
If A and B are conjugate matrices they have the same eigenvectors.
If A and B are conjugate matrices they have the same eigenvectors.
A and B are two m*n matrices. a. Show that B is invertible. b. Show that...
A and B are two m*n matrices. a. Show that B is invertible. b. Show that Nullsp(A)=Nullsp(BA)
Hi, I know that if two matrices A and B are similar matrices then they must...
Hi, I know that if two matrices A and B are similar matrices then they must have the same eigenvalues with the same geometric multiplicities. However, I was wondering if that statement was equivalent. In order terms, if two matrices have the same eigenvalues with the same geometric multiplicities, must they be similar? If not, is it always false?
Hi, I know that if two matrices A and B are similar matrices then they must...
Hi, I know that if two matrices A and B are similar matrices then they must have the same eigenvalues with the same geometric and algebraic multiplicities. However, I was wondering if that statement was equivalent. In order terms, if two matrices have the same eigenvalues with the same algebraic multiplicities, must they be similar? What about geometric multiplicities?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT