Orthogonally diagonalize each of the following symmetric matrices. Give the similarity transformation. (a) (c) [ 5 1 [ 3 1 ] ! ] [ 9 2 6 (b) ] 2 (d) [ 1.5 -0.5 ] -.5 1.5

Calc III Lec Day _ 10/_/16 Ch. 13.7 Tangent Plane Approximation and Differentials 1. The approximate change of a plane or line can described as the product of the partial derivatives and the amount the plane moved in that direction a. 2. The differential, or difference between the plane or line at an initial condition and at another condition, can then be written as the product of the partial derivatives and the paramedic derivatives a. Calc III Lec Day _ 10/_/16 Ch. 13.9 Lagrange Multipliers 1. For an equation g(x,y) = c the determiniation of extreme values for a condition, f(x,y), the extreme values will correspond to points where the gradients of f and g are parallel a.