# Linear Transformation Problem...

• Mar 20th 2007, 03:21 PM
ruprotein
Linear Transformation Problem...
JUst need someone to showme how to do this then it will defintly clarify the rest of the problems for me.. one of the few examples is

1- Show there exists a linear transofrmation T: R2→R3 such that T(1,1) = (1,0,2) and T(2,3) = (1,-1,4). What is T(8,11)?
• Mar 20th 2007, 03:25 PM
ThePerfectHacker
Quote:

Originally Posted by ruprotein
JUst need someone to showme how to do this then it will defintly clarify the rest of the problems for me.. one of the few examples is

1- Show there exists a linear transofrmation T: R2→R3 such that T(1,1) = (1,0,2) and T(2,3) = (1,-1,4). What is T(8,11)?

You can express,
[8,11]=2*[1,1]+3*[2,3]
Using the linearity property of the linear operator to get,
T(8,11)=2*T(1,1)+3*T(2,3)=2*[1,0,2]+3*[1,-1,4]
• Mar 20th 2007, 08:48 PM
CaptainBlack
Quote:

Originally Posted by ruprotein
JUst need someone to showme how to do this then it will defintly clarify the rest of the problems for me.. one of the few examples is

1- Show there exists a linear transofrmation T: R2→R3 such that T(1,1) = (1,0,2) and T(2,3) = (1,-1,4). What is T(8,11)?

Suppose T is that thransformation

T(1,0) = 3 T(1,1) - T(2,3) = (2, 1, 2)

T(0,1) = T(2,3) - 2 T(1,1) = (-1,-1, 0)

So the matrix M = (2, -1 ; 1, -1 ; 2, 0) does this job and so defines a linear
transformation with the required properties, hence a linear transformation
T exists with the required properties and is defined by the matrix M.

Hence T(8,11) = [M (8,11)']' = (5, -3, 16)

RonL