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2. Consider the following matrix and vectors. -) --() --(1) (:) --() -7 12 -18 B –18 23 -30 v1 = 2 (a) Show that vị and v2 are eigenvectors of B and find the corresponding eigenvalues. (b) Express v3 = в'0 03- [0, –4, –4]T as a linear combination of vi and v2, and hence compute

2. Consider the following matrix and vectors. -) --() --(1) (:) --() -7 12 -18 B –18 23 -30 v1 = 2 (a) Show that vị and v2 are eigenvectors of B and find the corresponding eigenvalues. (b) Express v3 = в'0 03- [0, –4, –4]T as a linear combination of vi and v2, and hence compute

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CR: Review Exercises
Problem 15CR: For what values of a does the matrix A=[01a1] have the characteristics below? a A has eigenvalue of...
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So this should be a rather simple question as I've done most of the work for it, and I'm just confused as to the meaning of one simple part of the problem. On the third problem second part, I'm simply confused as to what B^10 is referring to, I've done the rest of the problem, and if it's simply B*v3 that's rather simple, but the B^10 has me paused, and I can't find anywhere in my notes as to what this denotes. Thank you! 

2. Consider the following matrix and vectors. -) --() --(1) (:) --() -7 12 -18 B –18 23 -30 v1 = 2 (a) Show that vị and v2 are eigenvectors of B and find the corresponding eigenvalues. (b) Express v3 = в'0 03- [0, –4, –4]T as a linear combination of vi and v2, and hence compute
Transcribed Image Text:2. Consider the following matrix and vectors. -) --() --(1) (:) --() -7 12 -18 B –18 23 -30 v1 = 2 (a) Show that vị and v2 are eigenvectors of B and find the corresponding eigenvalues. (b) Express v3 = в'0 03- [0, –4, –4]T as a linear combination of vi and v2, and hence compute
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