1. ## Matrices

The matrix ( 1 2) maps Q(1,2) to R(5,7).
(1 3)

Find the 2 x 2 matrix which maps R back to Q.

2. Originally Posted by Crystal09
The matrix ( 1 2) maps Q(1,2) to R(5,7).
(1 3)
I will guess that you meant to say the following:

Code:
The matrix [ 1 2 ]
[ 1 3 ] maps Q(1, 2) to R(5, 7)]
Find the 2 x 2 matrix which maps R back to Q.
If so, then note that, for Ax = b, you have A^(-1)Ax = A^(-1)b = x. So you need only find the matrix inverse.

3. hi

$\displaystyle \left[\begin{matrix} 1 & 2 \\ 1 & 3 \end{matrix}\right] \left[\begin{matrix} 1 \\ 2 \end{matrix}\right] = \left[\begin{matrix} 5 \\ 7 \end{matrix}\right]$

That is, a linear transformation described by the matrix A.

$\displaystyle A\vec{x}=\vec{b} \Rightarrow x=A^{-1}\vec{b}$

$\displaystyle A^{-1} = \left[\begin{matrix} 3 & -2 \\-1 & 1 \end{matrix}\right]$

$\displaystyle \left[\begin{matrix} 3 & -2 \\ -1 & 1 \end{matrix}\right] \left[\begin{matrix} 5 \\ 7 \end{matrix}\right] = \left[\begin{matrix} 1 \\ 2 \end{matrix}\right]$