# Math Help - linear mapping

1. ## linear mapping

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]

2. 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 $B_1={1,x,x^2,x^3,x^4}$ be the standard ordered basis of $V$. Let $W$ be the vector space of 2x3 matrices over $R$ with the usual addition of matrices and scalar multiplication. Let $B_2$ be the ordered basis of $W$ given as follows:

$v_1=\left[\begin{array}{ccc} 1 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right]$

$v_2=\left[\begin{array}{ccc} 0 & 1 & 0 \\ 0 & 0 & 0 \end{array}\right]$

$v_3=\left[\begin{array}{ccc} 0 & 0 & 1 \\ 0 & 0 & 0 \end{array}\right]$

$v_4=\left[\begin{array}{ccc} 0 & 0 & 0 \\ 1 & 0 & 0 \end{array}\right]$

$v_5=\left[\begin{array}{ccc} 0 & 0 & 0 \\ 0 & 1 & 0 \end{array}\right]$

$v_6=\left[\begin{array}{ccc} 0 & 0 & 0 \\ 0 & 0 & 1 \end{array}\right]$

$B_2=\left\{\begin{array}{cccccc}v_1&v_2&v_3&v_4&v_ 5&v_6\end{array}\right\}$

Define $T:\rightarrow W$ by:

For $f=a_0+a_1x+a_2x^2+a_3x^3+a_4x^4$, put

$T(f)=\left[\begin{array}{ccc} 0 & a_3 & a_2+a_4 \\ a_1+a_0 & a_0 & 0 \end{array}\right]$

Construct the matrix $A=[T]_{B_1,B_2}$ that represent $T$ with respect to the pair $B_1, B_2$ of ordered bases.

I have no idea what this is supposed to mean, though.