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A First Course in Linear Algebra

  • by Robert A. Beezer
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  •   117
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Title
Chapter: 6 / Q: C22
Without using a calculator, find the eigenvalues of the matrix B
Chapter: 6 / Q: C23
Find the eigenvalues, eigenspaces, algebraic and geometric multiplicities for A =
Chapter: 6 / Q: C24
Find the eigenvalues, eigenspaces, algebraic and geometric multiplicities for A =
Chapter: 6 / Q: C25
Find the eigenvalues, eigenspaces, algebraic and geometric multiplicities for the 3 × 3 identity matrix I3. Do your results make sense?
Chapter: 6 / Q: C26
For matrix A =
Chapter: 6 / Q: C27
For matrix A =
Chapter: 6 / Q: M60
Repeat Example CAEHW by choosing x =
Chapter: 5 / Q: T10
A matrix A is idempotent if A2 = A. Show that the only possible eigenvalues of an idempotent matrix are λ = 0 and λ = 1. Then give an example of a matrix that is idempotent and has both of these two values as eigenvalues
Chapter: 6 / Q: T15
The characteristic polynomial of the square matrix A is usually defined as rA(x) = det (xIn A)
Chapter: 6 / Q: T20
Suppose that λ and ρ are two different eigenvalues of the square matrix A. Prove that the intersection of the eigenspaces for these two eigenvalues is trivial
total questions: 117
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