# Vector space help

1. Oct 13, 2006

### elle

Vector space help plz..

Hi,
Just started a linear algebra course recently but I am confused with the notation used

http://i9.tinypic.com/2w4za50.jpg

I am unsure how to proceed with this question. Can someone help? The part highlighted, what does it mean? 2x2 matrix of P? The P represents the polynomial entries? Can give me an example to give me a head start? Many thanks!

2. Oct 13, 2006

### radou

3. Oct 13, 2006

### elle

4. Oct 13, 2006

### radou

Yes, it's exactly something like this. Now just look at the definition of a vector space and at the properties that the addition and scalar multiplication must satisfy to proove if it's a vector space or not.

5. Oct 13, 2006

### elle

thanks for the confirmation again

Ok hmm I don't know if I'm on the right track but do I have to have two different matrices? Lets say matrix A and matrix B where A has elements:

http://i10.tinypic.com/4g7c4lj.jpg

and B with similar elements in order to check whether they satisfy closure by addition and multiplication? Or have I interpreted the definition totally wrong? :uhh:

6. Oct 14, 2006

### radou

You're on the right track.

7. Oct 14, 2006

### elle

Thanks

I've just noticed that I've chosen specific polynomials for my matrix entries so is that wrong? what would the matrix look like with general polynomial entries if a degree isn't given? Hmm am i making any sense here :uhh:

8. Oct 14, 2006

### radou

You don't have to write down specific polynomials as entries in your matrix. It is enough to write down something like $$\left(\begin{array}{cc}p_{1} & p_{2}\\p_{3} & p_{4}\end{array}\right)$$, where $$p_{i}, i = 1, \cdots, 4$$ are your real polynomials, which is the only thing that matters, unlike their degrees.

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