1. ## linear transformation

getting ready for final need some help
(1) 1
Question: R squared through R cubed is a linear transformation.if T(1)= (1),
1 1
T(1 = (0) find T(2)
-1) 1 (4)

have no idea

2. Originally Posted by fatboy
getting ready for final need some help
(1) 1
Question: R squared through R cubed is a linear transformation.if T(1)= (1),
1 1
T(1 = (0) find T(2)
-1) 1 (4)

have no idea
This is completely illegible as it stands. I think you mean something like "If $\displaystyle T\begin{bmatrix}1\\1\end{bmatrix} = \begin{bmatrix}?\\?\\?\end{bmatrix}$ and $\displaystyle T\begin{bmatrix}1\\-1\end{bmatrix} = \begin{bmatrix}?\\?\\?\end{bmatrix}$, find $\displaystyle T\begin{bmatrix}2\\4\end{bmatrix}$."

I suggest you repeat the problem, writing the vectors as rows rather than columns. This will be a lot easier to read.

3. yea sorry about that i dont know how to write like that on my computer, but the way you did it is the right question. the first row is 1,1,1 and the second is 1,0,1 is the question marks you put in.

4. Originally Posted by fatboy
yea sorry about that i dont know how to write like that on my computer, but the way you did it is the right question. the first row is 1,1,1 and the second is 1,0,1 is the question marks you put in.
$\displaystyle T\begin{bmatrix}1\\1\end{bmatrix} = \begin{bmatrix}1\\1\\1\end{bmatrix}$

$\displaystyle T\begin{bmatrix}1\\-1\end{bmatrix} = \begin{bmatrix}1\\0\\1\end{bmatrix}$

we need to solve a(1,1)+b(1,-1)=(x,y)

This gives the system

$\displaystyle a+b=x$
$\displaystyle a-b=y$

Solving gives

$\displaystyle a=\frac{x+y}{2}, \mbox{ and } b=\frac{x-y}{2}$

Now using the linear property of transforms on a(1,1)+b(1,-1)=(x,y) we get

$\displaystyle T(x,y)=T[a(1,1)+b(1,-1)]=T[a(1,1)]+T[b(1,-1)]=aT(1,1)+bT(1,-1)$

$\displaystyle T(x,y)=a(1,1,1)+b(1,0,1)=\left(\frac{x+y}{2},\frac {x+y}{2},\frac{x+y}{2} \right)+\left( \frac{x-y}{2},0,\frac{x-y}{2}\right)$

$\displaystyle T(x,y)=\left( x, \frac{x+y}{2},x\right)$

Now we can use this to find T(2,4)

$\displaystyle T(2,4)=\left( 2, \frac{2+4}{2},2\right)=(2,3,2)$

5. Here is the link to the La Tex help forum

http://www.mathhelpforum.com/math-help/latex-help/

Here is a link to a few different sites with code