(a) Find the eigenvalues and corresponding eigenvectors of the matrix A=(121). (b) Find P such that...

 

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(a) Find the eigenvalues and corresponding eigenvectors of the matrix A=(121). (b) Find P such that P-¹APD is diagonal. (c) Use the equation A" = PD"P-1 to find formulas for the entries in A". (d) A sequence ro, ₁.... ....of integers satisfies n+1 = 12rn-1+n for n 2 1. Suppose that ro = 0, ₁ = 1. Use A" to find a formula for In (e) How would the formula for 2, change if the sequence began with 20 = 1, ₁ = 0? (a) Find the eigenvalues and corresponding eigenvectors of the matrix A=(121). (b) Find P such that P-¹APD is diagonal. (c) Use the equation A" = PD"P-1 to find formulas for the entries in A". (d) A sequence ro, ₁.... ....of integers satisfies n+1 = 12rn-1+n for n 2 1. Suppose that ro = 0, ₁ = 1. Use A" to find a formula for In (e) How would the formula for 2, change if the sequence began with 20 = 1, ₁ = 0? (a) Find the eigenvalues and corresponding eigenvectors of the matrix A=(121). (b) Find P such that P-¹APD is diagonal. (c) Use the equation A" = PD"P-1 to find formulas for the entries in A". (d) A sequence ro, ₁.... ....of integers satisfies n+1 = 12rn-1+n for n 2 1. Suppose that ro = 0, ₁ = 1. Use A" to find a formula for In (e) How would the formula for 2, change if the sequence began with 20 = 1, ₁ = 0?

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a To find the eigenvalues and corresponding eigenvectors of the matrix A 4 1 2 1 We need to solve the characteristic equation A I 0 where is the eigen... View the full answer