Solve question 5 from Advanced Linear Algebra and the topic is

Question

Solve question 5 from Advanced Linear Algebra and the topic is

from inner product spaces dealing with orthonormal basis . Give a detailed solution with all necessary steps .

5 . Let A EC ( RS) where R’ has the standard inner product and A =
quot; TO
NONO
( 1 ) Show that A is definite positive quot;
( 2 ) Find an orthonormal basis of IR of eigenvectors of A .
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