1. Verify that the eigenvalues of A are: 2. (3 points) Verify that If these numbers...

 

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1. Verify that the eigenvalues of A are: 2. (3 points) Verify that If these numbers look familiar, it's because A is called the Golden Ratio, often denoted by y, and A is 1 - p, or p. H 3. (6 points) Diagonalize A by writing A = PDP-1 for a diagonal matrix D and an invertible matrix P. Ano and your answer from the previous part to verify the formula: and [79] 1 _1+5 X= 1- 5 2 2 4. (6 points) Use the fact that in = A = are eigenvectors for the eigenvalues A and A2 respectively. 1 1+ 1- 5 - - * (+~^) - (-~-~^). an 5 2 1 5 2 5. (2 points) Use this formula and a calculator to find the 45th term of the Fibonacci sequence. n 1. Verify that the eigenvalues of A are: 2. (3 points) Verify that If these numbers look familiar, it's because A is called the Golden Ratio, often denoted by y, and A is 1 - p, or p. H 3. (6 points) Diagonalize A by writing A = PDP-1 for a diagonal matrix D and an invertible matrix P. Ano and your answer from the previous part to verify the formula: and [79] 1 _1+5 X= 1- 5 2 2 4. (6 points) Use the fact that in = A = are eigenvectors for the eigenvalues A and A2 respectively. 1 1+ 1- 5 - - * (+~^) - (-~-~^). an 5 2 1 5 2 5. (2 points) Use this formula and a calculator to find the 45th term of the Fibonacci sequence. n