Linear algebra: Kernel/range

  • Thread starter Mdhiggenz
  • Start date
  • #1
327
1

Homework Statement



Determine the kernel/range of each of the following linear operators on R3

L(X)=(x1,x1,x1)T


Homework Equations





The Attempt at a Solution



So first thing I did was create a 3x1 matrix filled with ones.

I equaled it to zero and found x1=0 to be a solution. However I'm not quite sure how they come up with the following answer.

(0,x2,x3). Also why would it be a 2 dimensional subspace? Would it be due to x1 being zero?

Thanks
 
Last edited by a moderator:

Answers and Replies

  • #2
jbunniii
Science Advisor
Homework Helper
Insights Author
Gold Member
3,473
255

Homework Statement



Determine the kernel/range of each of the following linear operators on R3

L(X)=(x1,x1,x1)T

So first thing I did was create a 3x1 matrix filled with ones.

I equaled it to zero and found x1=0 to be a solution. However I'm not quite sure how they come up with the following answer.

(0,x2,x3). Also why would it be a 2 dimensional subspace? Would it be due to x1 being zero?
x1 = 0 if and only if the vector is of the form (0,x2,x3). The subspace spanned by vectors of this form has dimension 2 because for example {(0,1,0), (0,0, 1)} is a basis.
 
  • #3
327
1
Perfect explanation. Thank you!
 

Related Threads on Linear algebra: Kernel/range

  • Last Post
Replies
9
Views
1K
M
Replies
5
Views
844
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
2
Views
1K
Replies
3
Views
18K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
3
Views
13K
  • Last Post
Replies
7
Views
3K
Replies
1
Views
561
  • Last Post
Replies
3
Views
5K
Top