2. Gaussian Elimination

Theorem 2.1 (Gaussian Elimination with Back Substitution). Suppose that A is an nonsingular matrix; there exists an equivalent system where U is an upper-triangular matrix with . After U and Y are constructed, back substitution can be used to solve for X.

Theorem 2.1 (Gaussian Elimination with Back Substitution). Suppose that A is an nonsingular matrix; there exists an equivalent system where U is an upper-triangular matrix with . After U and Y are constructed, back substitution can be used to solve for X.