Determine the standard matrix of T Let T R2 Rightarrow R2 b

Determine the standard matrix of T

Let T : R2 Rightarrow R2 be the linear transformation such that T([3 1])= [1 4] and T([-5 -2])= [2 2]. Determine the standard matrix of T.

Solution

Let T : IRn IRm be a linear transformation. Then there exists an unique matrix A so that T(x) = Ax for all x in IRn , where A = ( T(e1) · · · T(en) ) and ej is the jth column of the identity matrix in IRn The matrix A is called the standard matrix for the linear transformation T

A = Te1 + Te2

= [ 1 2 ]

[ 4 2]