Question

Linear algebra help!

Answer 1

Let T be the operator on R^3 defined by:
T(x;y;z) = (x-y, y-x,x-z) and consider the vector:
\[v = \left(\begin{matrix}1 \\ 1\\2\end{matrix}\right)\]
and the basis..

Answer 2

and the basis:
B = {(1,0,1), (0,1,1),(1,1,0)}

Answer 3

a) Determine [T]b and [v]b
b) Compute [T(v)]b, and then verify that [T]b[v]b = [T(v)]b

Answer 4

So what don't you know how to do? T of b, v of b, or T of v of b?

Answer 5

actually all of those... i cant find a solved example.. all i need is a solution to a similar example..

Answer 6

So you want direction rather than a straight up answer?

Answer 7

yes.. not the answer. i have the answers i just want the steps..

Answer 8

my textbook sucks..

Answer 9

Heard that. Most collegiate math textbooks do. The douche bags that write them are trying to sell you an answer key as well. Lets start with [T]b.

Answer 10

T is considered a transformation for a given input, in this case, a matrix with three elements. As we will be performing T on b, you will be performing each given T operation on the given b element. What do you think we should do first?

Answer 11

hmm was it something like:
(1 0 1)(a1) (1)
(0 1 1)(a2)=(1)
(1 1 0)(a3) (2)

Answer 12

I believe what you are thinking of is the linear transformation Ax=B; where you are commonly given A and B and told to solve for x. I don't believe that is what is being asked for here.

Answer 13

In this case, I don't believe we need v at all to calculate T of b.

Answer 14

i was looking at my example that the professor solved in class:
he also had a basis:
B = {u1,u2,u3}
vector:
v = (x1,x2,x3}
So then he said that:
[v]b = [a1,a2,a3] and
[x1,x2,x3] = a1*u1+a2*u2+a3*u3

Answer 15

let me see.. im working this out actually if i get the right answer then so far so good..

Answer 16

heres what he was doin

Answer 17

Ok. Let me know if the answer for [T]b is {(1,-1,0),(-1,1,0),(0,-1,1)}

Answer 18

[T]b is actually:
\[\left[\begin{matrix}1 & -3/2&1/2 \\ -1 & 1/2&1/2\\0&1/2&-1/2 \end{matrix}\right]\]

Answer 19

I got [v]b right, it was:
(1,1,0)

Answer 20

What's the title of your math book?

Answer 21

Matrix Analysis and Applied Linear Algebra by Carl D. Meyer

Answer 22

Found it. Where are we? Chapter 3? 4?

Answer 23

chapter 4

Answer 24

Excercise 4.7.8

Answer 25

Sorry. I know how to do this, I'm just unfamiliar with this man's notation. Can you tell me what the square brackets are meant to indicate? I interprated them as parenthesis in your OP.