Are the following properties true? Linear Algebra

  • Thread starter flyingpig
  • Start date
  • #1
2,571
1

Homework Statement



Let A be a matrix

Then the following is true or false. (No need to explain why)

a) rank(A) = rank(At)
b) dim(Nul(A)) = dim(Nul(At)



The Attempt at a Solution



They are both true false right? The transpose swaps their row and columns which makes them interchanged

rank(A) = dim(Nul(At)

rank(At) = dim(Nul(A))
 

Answers and Replies

  • #2
They are both true false right?
Greetings! I'm somewhat confused. Consider a 2 by 3 matrix; is rank(A) = rank(AT)?
 
  • #3
2,571
1
I meant to say "They are both false" right?
 
  • #4
Dick
Science Advisor
Homework Helper
26,258
619
Greetings! I'm somewhat confused. Consider a 2 by 3 matrix; is rank(A) = rank(AT)?
Row rank does equal column rank, doesn't it? Isn't this fairly well known?
 
  • #5
2,571
1
I have not learned RowSpace yet sorry, we cover that next term
 
  • #6
Dick
Science Advisor
Homework Helper
26,258
619
I have not learned RowSpace yet sorry, we cover that next term
Then you maybe haven't done the rank-nullity theorem either. Maybe you should save this question for next term?
 
  • #7
Row rank does equal column rank, doesn't it? Isn't this fairly well known?
Right right. I guess the point is that the rank of a matrix is simply the number of linearly independent columns (any 3x2 and any 2x3 matrix can both have at most 2 linearly independent columns). Does this help at all flyingpig?
 

Related Threads on Are the following properties true? Linear Algebra

Replies
15
Views
2K
  • Last Post
Replies
2
Views
7K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
3
Views
1K
Replies
11
Views
9K
Replies
3
Views
2K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
17
Views
1K
  • Last Post
Replies
1
Views
1K
Replies
4
Views
806
Top