In the following several gradients and Hessian matrices are given. Classify them based on the extremal lines they identify. Here are the classification rules as a reminder Ridge lines Valley lines grad f(x,y) | €2 21<0 grad f(x, y)||c 0<12 -2y2 -1 0 H= 0 Valley Line ;gradf 1 3 0 H = 0 -5y4 2 gradf = 3 Valley Line -2y2 1 0 H = ;gradf = 0 Not an Extremal Line [8] -2y2 -1 0 H = ;gradf = 0 [A] Ridge Line 0 H == ;gradf = 0 -5y2-6, Not an Extremal Line 3 0 H = ;gradf = 0 5y2+4] Not an Extremal Line []
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