- #1
henry3369
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Assume the mapping T: P2 -> P2 defined by:
T(a0 + a1t+a2t2) = 3a0 + (5a0 - 2a1)t + (4a1 + a2)t2
is linear.Find the matrix representation of T relative to the basis B = {1,t,t2}
My book says to first compute the images of the basis vector. This is the point where I'm stuck at because I'm not sure how the books arrives at the images:
T(b1) = T(1) = 3+5t
T(b2) = T(t) = -2t+4t2
T(b3) = T(t2) = t2
Where are these results coming from?
I don't understand where 1 is supposed to go to solve for T(1). I guess its the notation that is throwing me off. Usually when solving for a transformation, it has something such as T(x) = x^2, and you solve the transformation by substituting the value of the input for x. But now my input is 1 for an entire expression (a0 + a1t+a2t2)
T(a0 + a1t+a2t2) = 3a0 + (5a0 - 2a1)t + (4a1 + a2)t2
is linear.Find the matrix representation of T relative to the basis B = {1,t,t2}
My book says to first compute the images of the basis vector. This is the point where I'm stuck at because I'm not sure how the books arrives at the images:
T(b1) = T(1) = 3+5t
T(b2) = T(t) = -2t+4t2
T(b3) = T(t2) = t2
Where are these results coming from?
I don't understand where 1 is supposed to go to solve for T(1). I guess its the notation that is throwing me off. Usually when solving for a transformation, it has something such as T(x) = x^2, and you solve the transformation by substituting the value of the input for x. But now my input is 1 for an entire expression (a0 + a1t+a2t2)