You are Here: Home >< Maths

# Can anyone help me with linear transformations? watch

1. Define a linear transformation. T: --> R^2 by

T(p) = .

Find polynomials and in that span the kernel of T, and describe the range of T.

This is the definition of a linear transformation:

T(p+q) =

= +

= T(p) + T(q)

T(cp) =

= c= cT(p)

These are the polynomials and in :

T(p) = =

So p(0) = 0 and p(0) = 0...

I chose any two polynomials that met these requirments...so...

= x^2
= 2x^2

Range: R^2

2. (Original post by Artus)
I chose any two polynomials that met these requirments...so...

= x^2
= 2x^2

The range of T is R^2, because there are two rows in T(p)...

If is the set of polynomials of degree at most 2, then

consider . Is this in the kernal of T? And if so what's its representation in terms of the span you've proposed?
3. (Original post by ghostwalker)
If is the set of polynomials of degree at most 2, then

consider . Is this in the kernal of T? And if so what's its representation in terms of the span you've proposed?
Yes it is in the kernal of T....what span do you mean? I didn't propose any span...
4. (Original post by Artus)
Yes it is in the kernal of T....what span do you mean? I didn't propose any span...
In that case, I've no idea what you're doing with that P_1 and p_2.
5. (Original post by ghostwalker)
In that case, I've no idea what you're doing with that P_1 and p_2.
Oh...ok I get it now...yes I did propose a span....I'm sorry, I just noticed it ...

Yes, p = x will be in the span, because p(0) = 0 and p(0)=0...and that's in the span so...yes...

p = 1x + 0x ... Is that right?
6. (Original post by Artus)

p = 1x + 0x ... Is that right?
Right for what? I've no idea what you're trying to say with that.

Since "x" is in the kernal, it must be representably as a linear sum of the vectors that span the kernal, i.e. the p_1 and p_2 that you've proposed. Is it?
7. (Original post by ghostwalker)
Right for what? I've no idea what you're trying to say with that.

Since "x" is in the kernal, it must be representably as a linear sum of the vectors that span the kernal, i.e. the p_1 and p_2 that you've proposed. Is it?
I'm sorry, but I don't know what you mean....the question asks me to "Find polynomials p1 and p2 in P_2 that span the kernel of T"...since p(0)=0 for both entries...it means that any equation like p(x) = ax^2 will span the kernel...so I said p1 = x^2 and p2=2x^2... I could not understand what you want me to do with p = x ... can you clarify that please?
8. (Original post by Artus)
I'm sorry, but I don't know what you mean....the question asks me to "Find polynomials p1 and p2 in P_2 that span the kernel of T"...since p(0)=0 for both entries...it means that any equation like p(x) = ax^2 will span the kernel...so I said p1 = x^2 and p2=2x^2... I could not understand what you want me to do with p = x ... can you clarify that please?
You really need to go back to your text book and see what these terms mean and look at some elemetary examples.

If a set (A) of vectors spans a space (or subspace, which is what the kernal is), then every vector in that space (or subspace) can be written as a linear sum of the elements of A. That's what "spans" means.

E.g. in R^2, which can be represented by ordered pairs whose elements are in R, then every element can be written in terms of the spanning set {(1,0), (0,1)} for example.

If you had the element (3,5), then it can be written as 3(1,0) + 5(0,1) etc.
9. (Original post by ghostwalker)
You really need to go back to your text book and see what these terms mean and look at some elemetary examples.

If a set (A) of vectors spans a space (or subspace, which is what the kernal is), then every vector in that space (or subspace) can be written as a linear sum of the elements of A. That's what "spans" means.

E.g. in R^2, which can be represented by ordered pairs whose elements are in R, then every element can be written in terms of the spanning set {(1,0), (0,1)} for example.

If you had the element (3,5), then it can be written as 3(1,0) + 5(0,1) etc.
Actually I did read the textbook...but its the first time I'm studying this, so its not clear in my head...that's why I'm asking...is my answer right or wrong?
10. (Original post by Artus)
Actually I did read the textbook...but its the first time I'm studying this, so its not clear in my head...that's why I'm asking...is my answer right or wrong?
Well you posted a thread over a week ago on spans and virtually had it correct then, and now seem to have forgotten what it means.

You don't seem to have an understanding of what you're doing, and whilst this forum is here to help people, it's not a teaching forum, though some people are very generous in that department.

And referring back to your first post, the range of T is not R^2.

Seriously, you need to go back and get these concepts under your belt; just reading them won't help your understanding unless you look at examples in detail, making sure you understand them and do basic exercises with them.

The one you've posted isn't a difficult exercise.
11. (Original post by ghostwalker)
Well you posted a thread over a week ago on spans and virtually had it correct then, and now seem to have forgotten what it means.

You don't seem to have an understanding of what you're doing, and whilst this forum is here to help people, it's not a teaching forum, though some people are very generous in that department.

And referring back to your first post, the range of T is not R^2.

Seriously, you need to go back and get these concepts under your belt; just reading them won't help your understanding unless you look at examples in detail, making sure you understand them and do basic exercises with them.

The one you've posted isn't a difficult exercise.

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: March 28, 2011
The home of Results and Clearing

### 2,917

people online now

### 1,567,000

students helped last year
Today on TSR

### University open days

1. Sheffield Hallam University
Tue, 21 Aug '18
2. Bournemouth University
Wed, 22 Aug '18
3. University of Buckingham
Thu, 23 Aug '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams