SOLUTION: Let L: R^2 -> R^2 be a linear operator. If L((1,2)^T)=(-2,3)^T and L((1,-1)^T)=(5,2)^T determine the value of L((7,5)^T) The answer in the back of the book was (7,18)^T bu

Algebra ->  College  -> Linear Algebra -> SOLUTION: Let L: R^2 -> R^2 be a linear operator. If L((1,2)^T)=(-2,3)^T and L((1,-1)^T)=(5,2)^T determine the value of L((7,5)^T) The answer in the back of the book was (7,18)^T bu      Log On


   

Question 22538: Let L: R^2 -> R^2 be a linear operator. If
L((1,2)^T)=(-2,3)^T and L((1,-1)^T)=(5,2)^T
determine the value of L((7,5)^T)
The answer in the back of the book was (7,18)^T but I dont know the steps of how to get that solution
Answer by khwang(438) About Me  (Show Source):
You can put this solution on YOUR website!
L((1,2)^T)=(-2,3)^T and L((1,-1)^T)=(5,2)^T
determine the value of L((7,5)^T)
The answer in the back of the book was (7,18)^T
Solve : (7,5) = a(1,2) + b(1,-1)
We have a+b = 7
and 2a-b = 5.
Hence, a=4, b =3.

So,L((7,5)^T) = L(4(1,2)T + 3(1,-1)^T)
= 4 L ((1,2)^T) + 3 L ((1,-1)^T)
= ...
Note, {{1,2)^T,(1,-1)^T} forms a basis of R^2.
You have to work hard.

Kenny