Assume that a 3 x 3 matrix A has eigenvalues 21 = 1, 22=0.8, 23=0.6 With corresponding eigenvectors (1), v V₁ = v₂ = (3) och V3 = Let v = x1v1 + x2v2 + x3v3 be a linear combination of the three eigenvectors. (a) Which 3-vectors can be written as a linear combination of the three eigenvectors? (b) What A¹v₁, Av2, Av3 respectively Av? (n is an arbitrary integer) (c) What about Any 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

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