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Calculus exercise
Hi guys, can anyone help me with this exercise. My exam is coming soon and i need this exercise completed for compare with my results and feel sure :S
It says:
1)We define = f: P₂[R] > R^2x2 linear transformation whose transformation matrix in basis B and E' is:
Mf(over BE')=
[1...2..1]
[1...0...1]
[4...8..4]
[2...2...0]
Where B= {1, X, 2X^2 + 1} and E', the canonical basis of R^2x2.
a)Find subspaces Ker(f) and Im(f).
b)Using the matrix of change of coordinates, find Mf(over EE')  where E = {X^2, X, 1}.
2)The linear transformation T:R^3 > R^4, satisfies the following conditions:
T((1,0,0)) = (0,0,0,0).
T((0,2,1)) = T((3,0,2)) = (0,1,1,0).
a)If possible, find a formula for T(v) for all v ∈ R^3.
b)Identify a pair of bases of vector spaces domain and codomain respectively, and find the matrix of T with respect to those chosen bases.
Thanks!
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