In each case, show that T2 Tand find (as in the preceding exercise) an ordered basis B such that MB(T) has the form given (0)k is the k k zero matrix) (a) T P2 Pi where T(a bx cx2) a b c)(l x x2), MB(T) (b) T R3 R3where T a, b, c) (a 2b, 0,4b c), MB(T) (c) T M22 M22 where T 1 0 0 02

Question: In each case, show that T2 = Tand find (as in the preceding exercise) an ordered basis B such that MB(T) has the form given

In each case, show that T2 = Tand find (as in the preceding exercise) an ordered basis B such that MB(T) has the form given (0)k is the k Ã— k zero matrix).
(a) T: P2 †’ Pi where T(a + bx + cx2) =
{a - b + c)(l + x + x2), MB(T) =

(b) T:R3 †’ R3where T{a, b, c) =
(a + 2b, 0,4b + c), MB(T) =

[1 0 0 02

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b We first verify that T 2 T Given a b c in R 3 we have T 2 a b c Ta 2b 0 4b c a 2b 0 4b c Ta b c He... View full answer

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