Originally Posted by
mivanova 
Hi,
I posted this before but I think the formating was bad and I didn't get any help.
I am attaching the problem this time with hope that someone can help me.
Thank you so much![ATTACH]
Let's put this into LaTeX form:
Let
be the standard ordered basis of
. Let
be the vector space of 2x3 matrices over
with the usual addition of matrices and scalar multiplication. Let
be the ordered basis of
given as follows:
![v_1=\left[\begin{array}{ccc} 1 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right]](http://latex.codecogs.com/png.latex?v_1=\left[\begin{array}{ccc} 1 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right])
![v_2=\left[\begin{array}{ccc} 0 & 1 & 0 \\ 0 & 0 & 0 \end{array}\right]](http://latex.codecogs.com/png.latex?v_2=\left[\begin{array}{ccc} 0 & 1 & 0 \\ 0 & 0 & 0 \end{array}\right])
![v_3=\left[\begin{array}{ccc} 0 & 0 & 1 \\ 0 & 0 & 0 \end{array}\right]](http://latex.codecogs.com/png.latex?v_3=\left[\begin{array}{ccc} 0 & 0 & 1 \\ 0 & 0 & 0 \end{array}\right])
![v_4=\left[\begin{array}{ccc} 0 & 0 & 0 \\ 1 & 0 & 0 \end{array}\right]](http://latex.codecogs.com/png.latex?v_4=\left[\begin{array}{ccc} 0 & 0 & 0 \\ 1 & 0 & 0 \end{array}\right])
![v_5=\left[\begin{array}{ccc} 0 & 0 & 0 \\ 0 & 1 & 0 \end{array}\right]](http://latex.codecogs.com/png.latex?v_5=\left[\begin{array}{ccc} 0 & 0 & 0 \\ 0 & 1 & 0 \end{array}\right])
![v_6=\left[\begin{array}{ccc} 0 & 0 & 0 \\ 0 & 0 & 1 \end{array}\right]](http://latex.codecogs.com/png.latex?v_6=\left[\begin{array}{ccc} 0 & 0 & 0 \\ 0 & 0 & 1 \end{array}\right])
Define
by:
For
, put
![T(f)=\left[\begin{array}{ccc} 0 & a_3 & a_2+a_4 \\ a_1+a_0 & a_0 & 0 \end{array}\right]](http://latex.codecogs.com/png.latex?T(f)=\left[\begin{array}{ccc} 0 & a_3 & a_2+a_4 \\ a_1+a_0 & a_0 & 0 \end{array}\right])
Construct the matrix
![A=[T]_{B_1,B_2}](http://latex.codecogs.com/png.latex?A=[T]_{B_1,B_2})
that represent
with respect to the pair
of ordered bases.
I have no idea what this is supposed to mean, though.
LinkBack URL
About LinkBacks
linear mapping
