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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A: Consider  matrix Applying Then  becomes Then  can be written as

Q: Suppose the 3 × 3 matrix A has eigenvalues λ1 = −6, λ2 = −2, and λ3 = 5.

A: according to guidelines we can solved only first 3 subparts thank you   We have the eigen values of…

Q: Find the eigenvalues and eigenfactor for the two by two matrix [0,1;-2,1]

A: Step 1:Step 2: Step 3:

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Q: 3. The characteristic polynomial of the matrix A = -1 4 -1 4 -1 is (A-2)(X - 5)². a) Find the…

A: Dear students as per our guidelines we can solve only first 3 questions. So kindly resubmit…