Let A be a symmetric 2 2 matrix and let be a nonzero scalar for which the equation xTAx is consistent Show that the corresponding conic section will be nondegenerate if and only if A is nonsingular

Question: Let A be a symmetric 2 2 matrix and let be a nonzero scalar for which the equation xTAx = is consistent.

Let A be a symmetric 2 × 2 matrix and let α be a nonzero scalar for which the equation xTAx = α is consistent. Show that the corresponding conic section will be nondegenerate if and only if A is nonsingular.

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