1 1 1 Show that the matrix A= -3 2 1 satisfies (Arl) = 0 for...

  

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1 1 1 Show that the matrix A= -3 2 1 satisfies (Arl) = 0 for some number r and some positive integer k and use this fact to determine the 93-5 matrix e At Hint: Compute the characteristic polynomial and use the Cayley-Hamilton theorem. Substitute the value of r and the smallest value of k that solve the equation. 11 1 -3-2 1 9 3-5 1 0 0 - 0 1 0 = 0 001 What is e e At = At? 1 1 1 Show that the matrix A= -3 2 1 satisfies (Arl) = 0 for some number r and some positive integer k and use this fact to determine the 93-5 matrix e At Hint: Compute the characteristic polynomial and use the Cayley-Hamilton theorem. Substitute the value of r and the smallest value of k that solve the equation. 11 1 -3-2 1 9 3-5 1 0 0 - 0 1 0 = 0 001 What is e e At = At?