(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 solution of the LU-factorization from i) above, determine the following systems of equations. 3a1 -2a2 + 0a3 = -1 -2a1 +2a2 + 1a3 = 7 0a1 + 1a2 + 2a3 = 12

Question

(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 solution of the LU-factorization from i) above, determine the following systems of equations.

3a₁ -2a₂ + 0a₃ = -1

-2a₁ +2a₂ + 1a₃ = 7

0a₁ + 1a₂ + 2a₃ = 12

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