Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,691

Quote by dzimitry
1. The problem statement, all variables and given/known data
find T(v) using the matrix relative to B and B'
T(x, y, z) = (2x, x + y, y + z, x + z)
v = (1, 5, 2)
B = { (2, 0, 1), (0, 2, 1), (1, 2, 1) }
B' = { (1, 0, 0, 1), (0, 1, 0, 1), (1, 0, 1, 0), (1, 1, 0, 0) }
2. Relevant equations
3. The attempt at a solution
T(2, 0, 1) = (4, 2, 1, 3)
= 4(1, 0, 0, 1) + 2(0, 1, 0, 1) + 1(1, 0, 1, 0) + 3(1, 1, 0, 0)

No, (4, 2, 1, 3) is NOT equal to (8, 5, 1, 6)! You are doing this backwards. You want to find numbers, a, b, c, d, such that (4, 2, 1, 3)= a(1, 0, 0, 1)+ b(0, 1, 0, 1)+ c(1 , 0, 1, 0)+ d(1, 1, 0, 0). That is you jeed to solve a+ c+ d= 4, b+ d= 2, c= 1, and a+ b= 3.
Then
[tex]\begin{bmatrix}a \\ b\\ c\\ d\end{bmatrix}[/tex]
will be the first column of the matrix.
= (8, 5, 1, 6)
T(0, 2, 1) = (0, 2, 3, 1)
= (4, 3, 3, 2)
T(1, 2, 1) = (2, 3, 3, 2)
= (7, 5, 3, 5)
A = 8 4 7
5 3 5
1 3 3
6 2 5
Av = (2, 0, 8, 6)
but if the person I am checking against is right, the answer should be (2, 4, 3, 3)
I am confused as to if I can even use the method I am using in this case.
Thanks in advance
1. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution

