Question
Asked Mar 4, 2020
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Prove the corollary to Theorem 6.41.
Hints:
(a) Prove that
BAB, =
-q 0 0 -p)
where
a +b
a – b
q =
and
2
(b) Show that q = 0 by using the fact that BAB, is self-adjoint.
(c) Apply Theorem 6.40 to
to show that p = 1.
Theorem 6.41. There exist nonzero scalars a and b such that
(a) T;LĄT,(wi) = aw2.
(b) T;LAT,(w2) = bw1.
Theorem 6.40. If <LA(w), w> = 0 for some w e R4, then
(TLAT,(w), w) = 0.
2.
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Prove the corollary to Theorem 6.41. Hints: (a) Prove that BAB, = -q 0 0 -p) where a +b a – b q = and 2 (b) Show that q = 0 by using the fact that BAB, is self-adjoint. (c) Apply Theorem 6.40 to to show that p = 1. Theorem 6.41. There exist nonzero scalars a and b such that (a) T;LĄT,(wi) = aw2. (b) T;LAT,(w2) = bw1. Theorem 6.40. If <LA(w), w> = 0 for some w e R4, then (TLAT,(w), w) = 0. 2.

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