# linear transformation to matrix

• Feb 2nd 2011, 11:25 PM
Taurus3
linear transformation to matrix
1. Let T:R2 -> R2 be the linear transformation which stretches vectors by a factor of 2 along the x-axis and reflects vectors across the x-axis. Find the matrix associated with this transformation.

2. Let T:R2 -> R2 be the linear transformation which reflects vectors through the xy-plane. Find the matrix A associated with this transformation.

Just to be clear, I don't want an answer, but can you show me some basic steps on how to start for both problems? Thanks so much.
• Feb 3rd 2011, 12:30 AM
FernandoRevilla
Quote:

Originally Posted by Taurus3
1. Let T:R2 -> R2 be the linear transformation which stretches vectors by a factor of 2 along the x-axis and reflects vectors across the x-axis. Find the matrix associated with this transformation.

$T(1,0)=(2,0),\;T(0,1)=(0,-1)$

Quote:

2. Let T:R2 -> R2 be the linear transformation which reflects vectors through the xy-plane. Find the matrix A associated with this transformation.

Did you mean $T:\mathbb{R}^3\rightarrow \mathbb{R}^3$ ?

Fernando Revilla
• Feb 3rd 2011, 02:34 AM
Taurus3
why yes! Thank you.