Numerical & Advanced

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1.
If A = [[2, -1], [1, 3]], then A^(-1) using Cayley-Hamilton is:
2.
The system x + 2y + z = 5, 2x + 3y + z = 9, 4x + 7y + 3z = k has no solution when:
3.
If A is a 3x3 matrix with det(A) = 5, find det(A * adj(A)).
4.
If A = [[1, 2], [0, 1]] and B = A + A^2 + A^3 + ... + A^20, find the (1,2) entry of B.
5.
Evaluate: |1 w w^2; w w^2 1; w^2 1 w| where w is a complex cube root of unity.

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