Question 8 worth 3 points
Let
A=[[1,-3,2],[-3,4,-1],[2,5,3]] and
b=[[2],[4],[-4]].
Define a transformation
T:R^(3)longrightarrowR^(3) by
T(x)=Ax.
If possible, find a vector
x whose image under
T is
b. Otherwise, state that
b is not in the range transformation T.
Question 9 worth 3 points
Let
a_(1)=[[1],[2],[-3]],a_(2)=[[-3],[-4],[1]],a_(3)=[[2],[1],[6]], and
b=[[-1],[1],[2]].
Determine whether
b can be written as a linear combination of
a_(1),a_(2), and
a_(3). In other words, determine whether weights
x_(1),x_(2), and
x_(3) exist, such that
x_(1)a_(1)+x_(2)a_(2)+x_(3)a_(3)=b. Determine the weights
x_(1),x_(2), and
x_(3) if possible.
