[0 1 0] [0 0 1] [x y z] The above 3x3 matrix above has characteristic polynomial of B to be -λ^3 + 4λ^2 + 5λ + 6. i.Select values of x,y,x so the above characteristic polynomial is achieved. ii.Determine the inverse of the matrix above on the basis of the Cayley-Hamilton's theorem which states that every matrix fulfils its characteristics polynomial utilizing the above given characteristic polynomial or otherwise.
[0 1 0]
[0 0 1]
[x y z]
The above 3x3 matrix above has characteristic polynomial of B to be -λ^3 + 4λ^2 + 5λ + 6.
i.Select values of x,y,x so the above characteristic polynomial is achieved.
ii.Determine the inverse of the matrix above on the basis of the Cayley-Hamilton's theorem which states that every matrix fulfils its characteristics polynomial utilizing the above given characteristic polynomial or otherwise.
(3 -2 0)
(-2 2 1)
(0 1 2)
Above shows a 3x3 matrix.
i.Utitilizing elementary row operations, determine the LU factorization of the matrix above
ii.From the answer from i above,determine the solution of the system of equations below
3a1 -2a2 + 0a3 = -1
-2a1 +2a2 + 1a3 = 7
0a1 + 1a2 + 2a3 = 12
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