Mathematics, 19.05.2020 21:01 sregan07
(2) Define T : R 3 → R 3 by T x y z = 0 3 −2 1 −2 2 2 −6 5 x y z . Let V be the set of all vectors that are fixed by T, which means that V = {v ∈ R 3 : T(v) = v}. (a) Show, using the definition of subspace, that V is a subspace of R 3 . (b) Come up with an equation that also defines V. (In other words, find a linear equation ax + by + cz = d such that x y z ∈ V ⇔ ax + by + cz = d.) (c) Geometrically, what kind of object is V (point/line/plane etc)? (d) Find a basis for V.
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(2) Define T : R 3 → R 3 by T x y z = 0 3 −2 1 −2 2 2 −6 5 x y z . L...
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