Cayley-Hamilton theorem
General · Mathematics
Study notes
Q: Use Cayley-Hamilton to find the inverse of [[2,1],[1,2]]. χ(λ) = λ²-4λ+3. So A²-4A+3I = 0. A²-4A = -3I: A(A-4I) = -3I. A⁻¹ = -(A-4I)/3 = (4I-A)/3. = (1/3)[[2,-1],[-1,2]] ✓! Check: A·A⁻¹ = I ✓!