Question 22538
 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