Linear Algebra (1 Viewer)

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Fpr the matrix find a basis for hte kernel and image of [itex} T_{A} [/itex] and find the rank and nullity of [itex] T_{A} [/itex]
T is a linear transformation


[tex] \left(\begin{array}{cccc} 2&1&-1&3 \\ 1&0&3&1 \\ 1&1&-4&2 \end{array} \right) [/tex]

the kernel of T simply means to find the null space of A right?
so when i row reduce i get
[tex] \left(\begin{array}{cccc} 1&0&3&1 \\ 0&1&-7&0 \\ 0&0&0&0 \end{array} \right) [/tex]

so do i simply find a 3x1 line matrix X such taht AX = 0
The image means something to do iwth the solution... but there is no augmented form given here... is there??

the basis of A will be the rank T right? Is base A = 2?? So the rank of T = 2?
the dimensio of the kernel is T is nullity of T... but i need to find the basis for the kernel first
 

0rthodontist

Science Advisor
1,230
0
The _rank_ of A will be the rank of T. Otherwise you are correct, what you need to do is find all the vectors x such that Ax = 0, from which you can extract a basis.
 
ok s oteh rank of kernel of T is 2

what about he nullity, though?? SO basically it asks how many vectors are forming the basis of th kernel?
 

0rthodontist

Science Advisor
1,230
0
No, the _dimension_ of the kernel of T is 2. That _is_ the nullity.
 
ok ok
so the number of independant rows in A: is the rank of A and that is 2
that is the tank of Ta yes?

also the rank of the kernel is the number of linearly independant vecotrs that can be formed from AX = 0 right

p.s. are you an orthodontist?
 

The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top