thanks for the help!
First: You can write these polynomials with respect to the basis
Thus we can write:
Put these vectors in a matrix and by performing elementary row-operations we get:
We see that span is a 3-dimensional subset and:
Now, letting:
:
is such that span( )= span( )
hey thank you for your help.
could u please send the operations you used to row reduce the matrix please.
when i did it i just did row 2 - 2 x row 1, row 3 - 4 x row 1, row 4 - row 1, row 5 - 13 x row 1, row 3 + 3x row 2
so im left with
1 0 1 1 0
0 1 0 -2 1
0 -3 -1 0 0
0 -1 -2 -10 5
i know that i am wrong because im not sure how to row reduce properly i dont think :-(
thanks for you help again.
oh right...fair enough lol.
umm i know row 2 is row 2 - 2 x row 1, dont know how the other rows came about?
can anyone help on the row reducing to get the final product.
sorry guys for this.
major thanks to the original helper and anyone else who may be able to help me out :-)
It's the same matrix with the 3 upper rows:
with and instead of the zero-rows.
Where are the vector representations of w.r.t. the basis
You want to show that is linear independant of . You can do that by showing that are linear independant, that is, the given matrix has rank 5. (meaning, having 5 linear independant rows).