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feinm1
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Homework Statement
Let B = {b1, b2, b3} be a basis for a vector space V and T : V -> R2 be a linear transformation with the property that
T(x1b1 + x2b2 + x3b3) =
2x1 - 4x2 + 5x3
0x1 - 1x2 + 3x3
Find the matrix for T relative to B and the standard basis for R2.
Homework Equations
[T(x)]C = M[x]B
Where M = [[T[b1)]C [T(b2)]C ... [[T(bn)]C
This matrix M is known as the matrix for T relative to the Bases B and C.
The Attempt at a Solution
[T(x)]C =
2x1 - 4x2 + 5x3
0x1 - 1x2 + 3x3
If [xB] =
|x1|
|x2|
|x3|
Then M =
|2 -4 5|
|0 -1 3|
Is this correct?