Question

Prove the following: Given k x m matrix A, m x n matrix B. Then rank(A)=m...

Prove the following: Given k x m matrix A, m x n matrix B. Then rank(A)=m --> rank(AB)=rank(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 A,B be a m by n matrix, Prove that |rank(A)-rank(B)|<=rank(A-B)
Let A,B be a m by n matrix, Prove that |rank(A)-rank(B)|<=rank(A-B)
Suppose A ∈ Mm×n(R) is a matrix with rank m. Show that there is an n...
Suppose A ∈ Mm×n(R) is a matrix with rank m. Show that there is an n × m matrix B such that AB = Im. (Hint: Try to determine columns of B one by one
In the system AX=b, where A is m x n matrix and rank of A is...
In the system AX=b, where A is m x n matrix and rank of A is m, you are given n vectors and among them p vectors are linearly dependent (p > m). Please write down the procedure to reduce the number of dependent vector by 1.
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.
Suppose we are given a system Ax = b, with A an n × m matrix....
Suppose we are given a system Ax = b, with A an n × m matrix. What can you say about the solution set of the system in the following cases? Provide a brief explanation. (i) rank(A) < n (ii) rank(A) = n (iii) rank(A) < m (iv) rank(A) = m
Let A be square matrix prove that A^2 = I if and only if rank(I+A)+rank(I-A)=n
Let A be square matrix prove that A^2 = I if and only if rank(I+A)+rank(I-A)=n
4.4.3. Suppose A and B are n × n matrices. Prove that, if AB is invertible,...
4.4.3. Suppose A and B are n × n matrices. Prove that, if AB is invertible, then A and B are both invertible. Do not use determinants, since we have not seen them yet. Hint: Use Lemma 4.4.4. Lemma 4.4.4. If A ∈ Mm,n(F) and B ∈ Mn,k(F), then rank(AB) ≤ rank(A) and rank(AB) ≤ rank(B).
Can i make conclusions about m x n matrix with rank r with (n-r) values and...
Can i make conclusions about m x n matrix with rank r with (n-r) values and it's solution number? Is there any other relations between rank of a matrix and avalaible solutions?
For n>=3 given the n x n matrix A with elements: A_ij=(i+j-2)^2. Determine the rank of...
For n>=3 given the n x n matrix A with elements: A_ij=(i+j-2)^2. Determine the rank of A.
Let A m×n be a given matrix with m > n. If the time taken to...
Let A m×n be a given matrix with m > n. If the time taken to compute the determinant of a square matrix of size j is j to the power 3, find upper bound on the a) total time taken to find the rank of A using determinants b) number of additions and multiplications required to determine the rank using the elimination procedure.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT