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Get Full Access to Linear Algebra With Applications - 1 Edition - Chapter 11.2 - Problem 12
Get Full Access to Linear Algebra With Applications - 1 Edition - Chapter 11.2 - Problem 12

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# In Exercises 712, determine if the given matrix is positive definite.A =1 2212 5 1 32 1

ISBN: 9780716786672 433

## Solution for problem 12 Chapter 11.2

Linear Algebra with Applications | 1st Edition

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Problem 12

In Exercises 712, determine if the given matrix is positive definite.A =1 2212 5 1 32 1 14 11 3 1 3

Step-by-Step Solution:
Step 1 of 3

Constant Coe¢ cient Homogeneeous DE. Case 1: Starting simple: Finding two Linearly independent solutions of Linear second order Constant Homogeneous DE s. Solutions to ▯ 2 ▯ 00 0 Ly = aD + bD + c y = ay + by + cy = 0: (1) Lets look at the simpler case of ▯ 2 ▯ 00 0 Ly = D + a D + 1 2 y = y + a y1+ a y 2 0: (2) 00 where the coe¢ cient of y is 1: To solve the homogeneous equation 00 0

Step 2 of 3

Step 3 of 3

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