## REMAINDER 3 years ago find the polynomial in P2 whose coordinate matrix with respect to the basis

1. REMAINDER

is|dw:1349421000654:dw|

2. REMAINDER

$B=\left\{ x+x ^{2} ,1+x\right\}$ this is the basis

3. REMAINDER

is it gonna be B=(0,0,0) ;(0,1,1);(0,1,0) |dw:1349421351446:dw| |dw:1349421421254:dw|

4. Coolsector

we need a matrix to make the change between the two basis

5. REMAINDER

how to find that matrix

6. Coolsector

well i have some problem here .. how can B be a basis for some R3 if it has only two vectors

7. REMAINDER

i think the firt vector is zero

8. Coolsector

it's given ?

9. Coolsector

but still i dont think it is a basis in this case

10. REMAINDER

no

11. Coolsector

i might dont understand the question but B isnt a basis for P2

12. Coolsector

we cant generate for example "1" which is a valid P2

13. REMAINDER

yes it is

14. Coolsector

how come ?

15. Coolsector

here i just showed you that it doesnt span P2

16. REMAINDER

we have been told

17. Coolsector

so i dont know .. i dont understand im sorry

18. REMAINDER

ok in general how to anser this kind of questions

19. Coolsector

you have to find a matrix that converts between the two basis and then you only have to multiply

20. REMAINDER

eg like wat i did

21. Coolsector

for example moving from S = { (1,2) , (3,5) } basis into the standard R2 basis the matrix is 1 3 2 5 now if you multiply this matrix with S vectors you get them in the standard R2 basis

22. Coolsector

im sorry i couldnt help more but i really dont know how

23. REMAINDER

ok thnx

24. SWAG

hmm

25. REMAINDER

@Coolsector i din't find the answer ,bul i'll try consult to my lecture