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Find the principal components of the data for Exercise 1

$u _ { 1 } \approx \left[ \begin{array} { c } { 0.05 } \\ { - 0.72 } \end{array} \right] , u _ { 2 } \approx \left[ \begin{array} { c } { 0.32 } \\ { 0.95 } \end{array} \right]$

Algebra

Chapter 7

Symmetric Matrices and Quadratic Forms

Section 5

Applications to Image Processing and Statistics

Introduction to Matrices

Campbell University

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

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Okay, So for this problem from progress exercise, we know that we have a co baroness Magics s equals 2 86 minus 27 minus two. Me seven the 16. So we just need to find out the AG a 1,000,000 Eigen vectors for these uncovering matrix. Also, the characteristic equation will be determined off. This matrix s minus slammed I equals zero. That gives us 86 minus on Lambda I'm 16 minus lambda minus 27. Square equals zero by Soviet Miss Quadratic equation. We have two solutions. Lambda One equal to 95 point to all for one and another that week was just a 6.795 night. Also, Lambda winds, the larger Eigen value corresponding Eigen Vector will be B one equals 20.9465 and the V two equals up and the minus 0.32 to 7. And as for of the two, we have O. C. R. Playing in 3227 in the minus 0.9465 And the V one corresponds to the larger Eigen value. So it's the principle components

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