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Worksheet: Cayley–Hamilton Theorem

Q1:

Consider the matrices

Find 𝐴 2 .

  • A 𝐴 = 7 1 0 1 5 2 2 2
  • B 𝐴 = 1 4 9 1 6 2
  • C 𝐴 = 7 6 9 2 2 2
  • D 𝐴 = 5 6 9 1 0 2
  • E 𝐴 = 1 4 9 1 6 2

Find 𝐴 + 3 𝐴 + 2 𝐼 2 .

  • A 𝐴 + 3 𝐴 + 2 𝐼 = 0 0 0 0 2
  • B 𝐴 + 3 𝐴 + 2 𝐼 = 1 2 0 0 1 2 2
  • C 𝐴 + 3 𝐴 + 2 𝐼 = 6 4 6 1 2 2
  • D 𝐴 + 3 𝐴 + 2 𝐼 = 4 1 6 0 6 2
  • E 𝐴 + 3 𝐴 + 2 𝐼 = 0 0 0 0 2