Determine if the system corresponding to the matrix below has a unique, infinitely many, or no solution. Explain your answer. If the solution exists, write the solution in terms of the pivot variables. You can assume the first, second, and third columns of the matrix correspond to the variables x, y, and z, respectively.

(a) [ 1 0 0 0 0 0 0 1 0 0 0 1 ]

(b) [ 1 0 0 2 0 1 0 3 0 0 1 2 ]

(c) [ 1 0 0 3 0 1 0 0 0 0 1 0 ]

(d) [ 1 0 1 5 0 0 0 0 0 0 1 0 ]

Find the inverse of the matrix [ 2 8 1 0 ] using Gauss Elimination

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