Attached as TheProblem.jpg.
xT A x is 0 when (x1, x2, x3) = (0,1,0) because of the zero on the diagonal. Actually, xT A x goes negative for x = (1, -10, 0) because the second pivot is negative.
xT A x
The Attempt at a Solution
I computed the product and got 9x22 + 4 x1x1 + 4x12.
I'm thinking that I might need to show that that obtained polynomial must be below zero since we want to show that matrix A is not a positive definite matrix but, I don't know where to go from here.
Any input would be appreciated!
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