H51 - Math 330 Homework 5.1 (Pages 308,309) (2) Is = 2 an...

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Unformatted text preview: Math 330 Homework 5.1 (Pages 308,309) (2) Is = 2 an eigenvalue of A = bracketleftBigg 3 2 2 8 bracketrightBigg ? Why or why not? SOLUTION: If there are nonzero vectors vectorx so that Avectorx = 2 vectorx then it means that A- 2 I has a nontrivial null space: A- 2 I = bracketleftBigg 1 2 2 6 bracketrightBigg However, this matrix is invertible since the rows are not multiples of each other. Therefore, 2 is not an eigenvalue. (4) Is bracketleftBigg- 1 + 2 1 bracketrightBigg an eigenvector of bracketleftBigg 2 1 1 4 bracketrightBigg ? If so, find the eigenvalue. SOLUTION: We check the matrix multiplication bracketleftBigg 2 1 1 4 bracketrightBiggbracketleftBigg- 1 + 2 1 bracketrightBigg = bracketleftBigg 2(- 1 + 2) + 1 (- 1 + 2) + 4 bracketrightBigg = bracketleftBigg- 1 + 2 2 3 + 2 bracketrightBigg If this is equivalent to matrix multiplication by some scalar then the second coordinate tells us that we must have = 3 + 2. If this is indeed the case then the same multiplier must2....
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This note was uploaded on 09/19/2009 for the course MATH 330 taught by Professor Johnson,j during the Spring '08 term at Nevada.

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H51 - Math 330 Homework 5.1 (Pages 308,309) (2) Is = 2 an...

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