- #1
margaret37
- 12
- 0
Homework Statement
Define T : R3x1 to R3x1 by T = (x1, x2,x3)T = (x1, x1+x2, x1+x2+x3)T
1 Show that T is a linear transformation
2 Find [T] the matrix of T relative to the standard basis.
3 Find the matrix [T]' relative to the basis
B' = {(1,0,0)t, (1,1,0)t, (1,1,1)t
4 Find the transition matrix Q from B to B'
5 Verify that [T]' = Q[T]Q-1
Homework Equations
The Attempt at a Solution
1) I think this is done I showed that T(c(alpha + beta)) = c* T(alpha) + T(Beta) by substituting in vectors (a1, a2, a3) and (b1,b2,b3) and working throught the algebra.
2) This is what I did, I think I understood this properly:
I built a transformation Matrix [T] = T(e1) | T(e2) | T(e3)
I got
1 0 0
1 1 0
1 1 1
3) Then I think is wrong but I'm not sure
I built another matrix [T]' = T(v1) | T(v2) | t(v3)
where v1, v2, and v3 are the the vectors given above
I got
1 1 1
1 2 2
2 2 3
4) Then I built a transformation matrix by finding the coordinates of e1, e2, and e3 relative to v1, v2 and v3
I got
1 -1 0
0 1 -1
0 0 1
I calculated an inverse
1 1 0
0 1 1
0 0 1
5) Then if I had done everything right
[T]' should have been equal to Q[T]Q-1
But it wasn't even close
1 1 1
0 1 1
0 0 1
Any help would be greatly appreciated.
Margaret