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Counterexample bank

Part C is won by knowing which tempting claims are false. 148 counterexamples; 85 free. The rest come with the Notes pack.

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#1 · Analysis & Linear Algebra › Inner Product Spaces and Forms

“Every real symmetric matrix is positive definite if det > 0” — false

Counterexample locked — unlock with Notes + PYQ

linear algebraquadratic forms

#2 · Analysis & Linear Algebra › Inner Product Spaces and Forms

“det A > 0 implies A is positive definite” — false

Counterexample: A = diag(−1, −1)

det = 1 > 0 but both eigenvalues are negative. All leading principal minors must be positive.

linear algebraquadratic forms