a b Consider the vector space W { : a %3D с d 3 let v = 4 -3 wo different ordered bases S and T for W. mine [v]s and [v]r•

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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a
Consider the vector space W
{
с d
: a + d = 0} of 2 × 2 matrices having trace
3
zero. Also let v =
4
-3
(2a) Find two different ordered bases S and T for W.
(2b) Determine [v]s and [v]r.
(2c) Determine Ps-T and QT-s and verify [v]s = Ps-T[v]T and [v]T = Qr-s[v]s-
Transcribed Image Text:a Consider the vector space W { с d : a + d = 0} of 2 × 2 matrices having trace 3 zero. Also let v = 4 -3 (2a) Find two different ordered bases S and T for W. (2b) Determine [v]s and [v]r. (2c) Determine Ps-T and QT-s and verify [v]s = Ps-T[v]T and [v]T = Qr-s[v]s-
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