Consider the matrix A=[3 -1; -1 3]. (a) Can the quadratic form x'*A*x evaluate to zero for some non-zero vector x? (x is a 2x1 column vector, and x' means x transposed: usual Matlab notation). (b) Does the equation A*x=b, b arbitrary, have a unique solution? If it does, prove it. (c) Show that the total potential energy f(x)=1/2*x'*A*x-b'*x has a minimum for x that solves the linear equations A*x=b.(adsbygoogle = window.adsbygoogle || []).push({});

This is the question which i'm approached with

my answer is as following

a) No, because it's a symetric matrix only x'Ax = 0 only if vector x = 0.

b) Yes , it is not underdetermined and det does not equal 0

c) iono

i was wondering what you guys thought

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# Total potential energy in matrix

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