Question

Determine the kernel and range of the transformation T(x,y,z) = (x,2x,y-z) R3--->R3

Answer 1

Can you tell what the matrix that represents this transformation is?

Answer 2

No

Answer 3

One way to see what the matrix of the transformation will be is to plug in the standard basis vectors for R^3. That would be (1,0,0), (0,1,0), and (0,0,1). What is T(1,0,0)?

Answer 4

(1,2,0)

Answer 5

Right. So the first column in your matrix is (1,2,0) (make sure to make it a column, not a row).

Answer 6

What is T(0,1,0)?

Answer 7

0,0,1

Answer 8

So thats the second column of the matrix. What about T(0,0,1)?

Answer 9

0,0,-1

Answer 10

So your matrix is:\[\left[\begin{array}{ccc}1&0&0\\2&0&0\\0&1&-1\end{array}\right]\]

Answer 11

he knows how to do the rest

Answer 12

ah, cool.

Answer 13

I do?

Answer 14

we just did it

Answer 15

the last problem was find kernel and range. now that you have the marix find kernel and range

Answer 16

right?

Answer 17

nonono give joe the medal, Im not trying to highjack I just forgot this stuff so want to stick with your questions:)

Answer 18

@zzr0ck3r @joemath314159 I consider myself mathematically literate, just sometimes these abstract things are easy to get rusty with. I appreciate the help :)

Answer 19

if we know how to do it, what's the point of learning it:) I have taken 200,300 linear algebra classes and every time I get a question with this stuff I have to think for a while, or find my notes. especially the change of bases stuff.