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(Solved): Question 8 worth 3 points Let A=[[1,-3,2],[-3,4,-1],[2,5,3]] and b=[[2],[4],[-4]]. Define a transfor ...



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.

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