Linear Transformation S: Matrix A, Injective/Surjective

[orange12]

Let the vectors a1,a2,a3 €R3 and b1,b2,b3 € R4 be given by

a1 a2 a3
1 -2 3
2 2 1
1 1 2

b1 b2 b3
1 1 -1
2 -3 2
1 4 3
3 -2 1

The linear transformation S : R3 --> R4 is defined by

S(x)= b1a1Tx+b2a2Tx+b3a3Tx x€R3

1. Find the standard matrix A for the linear transformation S og decide if the linear transformation S er injective or surjective.

 

[rochfor1]

I smell homework. Tell us what you've tried.

 

[HallsofIvy]

What is "b1a1T" and the others? That should be easy to find.

 

[orange12]

What is "b1a1T" and the others? That should be easy to find.

I have tried to put the a1,a2 etc and b1,b2 etc into the formula for S(x).

First i put out x so it became

S(x)=(b1a1T+b2a2T+b3a3T)x, and then i get a Matrix, but i am not sure that it is the standard matrix. I read in my book that u have to see what it does to the Idendity colums, but can't figure out how to do that. I have tried out some things, but it would help a lot if you could show me which way is the right way to do it.