Basis Matrix

**tttcomrader** · November 22nd 2008, 02:35 PM

I was tutoring yesterday and I got caught completely offguard by this question:

Let $B= \{ 1+t^2,3-t+4t^2,-1+2t-4t^2 \}$

Find $[1-3t+5t^2]_B$ and find q such that [tex]q_B = (1,3,-2)

I forgot most of my linear algebra, and I don't have my notes with me, would anyone please explain this to me? Thanks.

**Plato** · November 22nd 2008, 03:38 PM

You want, $1 - 3t + 5t^2 = a\left( {1 + t^2 } \right) + b\left( {3 - t + 4t^2 } \right) + c\left( {1 + 2t - 4t^2 } \right)$ .
So
$\begin{gathered} a + 3b + c = 1 \hfill \\ - b + 2c = - 3 \hfill \\ a + 4b - 4c = 5 \hfill \\ \end{gathered} $
SOLVE!

Thread: Basis Matrix

LinkBack

Thread Tools

Display

Basis Matrix

Similar Math Help Forum Discussions

The basis of a matrix

matrix and basis

matrix A for T with respect to the basis B.

Matrix/basis question

basis for matrix

Search Tags