Please use Matlab fomat.
(Use format rat) Recall [x]B denotes the coordinate vector of x with respect to a basis B for a vector space V . Given two bases B and C for V , P C < B denotes the change of coordinates matrix, which has the property that
P_C < B [x]B = [x]C for all x ∈ V.
It follows that
P_ B < C = (P_ C < B)^-1 .
Also, if we have three bases B, C, and D,
then (P_D < C)(P_C <B) = P_D < B .
Each of the following three sets is a basis for the vector space P3:
ε = {1, t, t^2 , t^3 } ,
B = {1, 1 + 2t, 2 − t + 3t^2 , 4 − t + t^3 } , and
C = {1 + 3t + t^3 , 2 + t, 3t − t^2 + 4t^3 , 3t} .
(a) Find and enter the matrices P = P_ε < B and Q = P_ ε < C