Final answer:
The LU factorization is a method used to factorize a square matrix into the product of two matrices: a lower triangular matrix (L) and an upper triangular matrix (U). By performing Gaussian elimination on the matrix, we can find the LU factorization. The system of equations can then be solved by substituting the LU factorization back into the equations and solving for the unknowns.
Step-by-step explanation:
LU factorization is a method used to factorize a square matrix into the product of two matrices: a lower triangular matrix (L) and an upper triangular matrix (U). To find the LU factorization of a matrix, perform Gaussian elimination on the matrix by using row operations to eliminate variables. The resulting matrix will be the upper triangular matrix (U), with the lower triangular matrix (L) containing the multipliers used to create the upper triangular matrix. With the LU factorization, the system of equations can be solved by substituting the LU factorization of the matrix back into the system of equations and solving for the unknowns.