- 1 3 -1 3 det(A - AI) det 2 1. |1 - i -1 - A 3 2 0 1- a To find the determinant, expand along the first row and substitute the appropriate expressions from the matrix. det(A - il) a11det(A11) – a12det(A12) + a13det(A13) det(A,,) – (0)det(A12) + det(A13) Now, find the required submatrices that have nonzero coefficients in the above equation. det(A,) = (-1 – 4)(I - 1) - (3)(0) (1 + i)(1 – 1) det(A,3) = (3)(0) – (-1 – 4)(2) )ca + 3)

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