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Unformatted text preview: 1 2 3 1 1 2 1 2 . Find the inverse of A . / 10 1 2 2 2. (10 Points) Let A = 1 2 3 1 1 2 1 1 . Find a basis for C ( A ) and for N ( A ). / 10 2 3 3 3. (10 Points) Let f ± x y ² = 3 x 2 + 12 x + 4 y 36 y 2 + 5 . Find all critical points of f and classify them (that is, determine whether each is a local maximum, a local minimum, or a saddle point). / 10 3 4 4 4. (10 Points) Find the minimum value of f x y z = x 2 + y 2 + z 2 subject to the constraint that 3 x + 2 y + z = 6 . (There is only one critical point of the constrained function; you don’t need to test that it’s a minimum. But do make sure you state the value of the function at that critical point). / 10 4 5 5 5. (10 Points) Find the leastsquares line of best ﬁt for the three points ± 1 2 ² , ± 2 4 ² , ± 3 5 ² / 10 5 (This page intentionally left blank. You can use it for scratch work.) 6...
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 Spring '09
 MihaiBeligan
 Calculus, Linear Algebra, Algebra, Critical Point, Multivariable Calculus, scratch work

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