Linear Algebra Question with nullspace/rank/nullity

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Hi

I was just wondering if I'm right about this answer I got. Here is the math problem:
_____________________________________________________

Let T: R^3 (arrow pointing) P3 be the homomorphism

([a])
T() = (a-b) + (a-b)x + cx^2 + cx^3
([c])

Find the nullspace, nullity, and rank of T.
_____________________________________________________

N = DD - R
N = 3 - 3
N = 0

So nullity = 0, rank = 3

The nullspace is: (below the {a b c} moves over and doesn't line up but it is {a b c} stacked on top of each other. (Sorry about that)

{a}
N(h) = {b} in R^3 | (a-b) + (a-b)x + cx^2 + cx^3=(0-0) + (0-0)x + 0x^2 +0x^3
{c}

= 0 + 0x + 0x^2 + 0x^3

= (0)
(0)
(0)
*This is the zero vector I think*

I could be wrong about all this. If you could please let me know.

I would really appreciate it.

Take care,
Beckie
 
Anyone??? Please let me know if I need to present this problem better so its easier to read. I don't have special math software, so I don't know how to put in all the cool symbols, etc.

Thanks
Take care,
Beckie
 
Beckie said:
Anyone??? Please let me know if I need to present this problem better so its easier to read. I don't have special math software, so I don't know how to put in all the cool symbols, etc.

Thanks
Take care,
Beckie
Click to expand...

The way you have typed it is unclear.
 
I don't have special math software
Click to expand...

You don't need special math software, Becky, just a tutorial in LaTex.

It's available on the site or just click on quote at the upper right corner of the post to see the code.
 
First the mapping is from dim3 space to a dim4 space.
Also the matrix for T is \(\displaystyle \left[ {\begin{array}{rrr}
1 & -1 & 0 \\
1 & -1 & 0 \\
0 & 0 & 1 \\
0 & 0 & 1 \\
\end{array}} \right]\), also note that \(\displaystyle \left[ \begin{array}{l}
1 \\
1 \\
0 \\
\end{array} \right]\) spans the null space.
 
Here is a trial of me trying to do the LaTex stuff
\(\displaystyle \[T left ( \ [ {a} {b} {c} \right ] \ right ) . \ ]


i'm trying to see if I can use LaTex\)
 
Beckie, do a quote. Click the reply quote tab.
You will see my LaTeX.
 
\(\displaystyle \[T: R^3 \rightarrow P^3 be the homomorphism. \]\)
 
\(\displaystyle \[T: R^3 \rightarrow P^3 & be & the & homomorphism. \]\)
 
Sorry about all the strange posts. I was experimenting with LaTex.
 
You don't have to post your experiments. You can click 'preview' to see what they look like without posting.
 
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