Linear Algebra Proofs

  • #1
1) Find two matrices A and B where Rank [AB]≠Rank(BA)

2) Find a matrix A where Rref(A)≠Rref(A^T) where T is the transpose

3) Find X given that B is invertible if BXB^-1 –A=I_n (identity matrix)

4) Prove that [Ab_1 Ab_2 Ab_3] is linearly dependent given that {b1 b2 b3} is linearly dependent.

i cant get any of these and tried substituting numbers and nonzero rows and columns to obtain any of the four. Can someone please help me get these? Thank you to those who help in advance!
 

Answers and Replies

  • #2
0rthodontist
Science Advisor
1,230
0
1-2 is just a matter of trying more matrices. 3 is just algebra. For 4 you should use the definition of linear dependence.
 

Related Threads on Linear Algebra Proofs

  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
2
Views
967
  • Last Post
Replies
4
Views
3K
  • Last Post
Replies
7
Views
995
  • Last Post
Replies
3
Views
7K
  • Last Post
Replies
4
Views
5K
  • Last Post
Replies
6
Views
1K
Replies
6
Views
5K
Replies
8
Views
805
Replies
4
Views
7K
Top