Assume that a 3 x 3 matrix A has eigenvalues 21 = 1,22=0.8, 23=0.6 With corresponding eigenvectors (2), v₂ = (³) och (⁹). (a) Which 3-vectors can be written as a linear combination of the three eigenvectors? (b) What Av1, A2, Av3 respectively Av? (n is an arbitrary integer) (c) What about Anv when n→→∞o? (It depends a little on the coefficients x1, x2, x3) V₁ = V3 =

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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Assume that a 3 x 3 matrix A has eigenvalues 21 = 1,22=0.8, 23=0.6 With corresponding eigenvectors
(₂), v₂ = (³) och
(⁹).
(a) Which 3-vectors can be written as a linear combination of the three eigenvectors?
(b) What A¹v1, A2, Av3 respectively Av? (n is an arbitrary integer)
(c) What about Anv when n→ ∞o? (It depends a little on the coefficients x1, x2, x3)
(d) Now suppose that we have a 3×3 matrix with some eigenvalues 21, 22, 23 € R
V₁ =
V3 =
Transcribed Image Text:Assume that a 3 x 3 matrix A has eigenvalues 21 = 1,22=0.8, 23=0.6 With corresponding eigenvectors (₂), v₂ = (³) och (⁹). (a) Which 3-vectors can be written as a linear combination of the three eigenvectors? (b) What A¹v1, A2, Av3 respectively Av? (n is an arbitrary integer) (c) What about Anv when n→ ∞o? (It depends a little on the coefficients x1, x2, x3) (d) Now suppose that we have a 3×3 matrix with some eigenvalues 21, 22, 23 € R V₁ = V3 =
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