3. Let a linear equation system Ax = b with its coefficient matrix: 1 2 1 1 1 2 A = 2 1 3 b= 2 3 (a) Please find a lower triangular matrix L and an upper triangular matrix U so that matrix A can be represented as a product of LU. Such a representation of a matrix A is called as LU factorization. (b) Apply the result in (a) to solve the solution of Ax = b.

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