# 32 the system of differential equations is solution

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Unformatted text preview: _________________________________________________________________ page 375 —————————————————————————— CHAPTER 7. —— 26 . The general solution is x . ________________________________________________________________________ page 376 —————————————————————————— CHAPTER 7. —— . . 28 . We note that A . It follows that A I I 0 , for . A . . Suppose that and are linearly dependent. Then there exist constants and , not both zero, such that 0 Assume that It is clear that A I 0 On the other hand, A I 0 . Since , we must have . Note that A I , which leads to a contradiction. . ________________________________________________________________________ page 377 —————————————————————————— CHAPTER 7. —— . Let , with . Suppose that dependent. Then there exist constants , and , and are indeed linearly , not all zero, such that 0 It is clear that A Assume that other hand, A I I...
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## This note was uploaded on 03/11/2014 for the course MA 303 taught by Professor Staff during the Spring '08 term at Purdue.

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