Consider the system of linear equations, 2x 1 + 3x 2 - x 3 = 5 4x 1 + 4x 2 - 3x
ID: 2901502 • Letter: C
Question
Consider the system of linear equations,
2x1 + 3x2 - x3 = 5
4x1 + 4x2 - 3x3 = 3
-2x1 + 3x2 - x3 = 1
a) Write the system in the form of (A|b) and solve for x = (x1 , x2 , x3)T by Gaussian elimination (i.e. reduction to upper triangular form and back substitution, no pivoting).
b) Find the LU factorization of A and solve for x by forward and back substitution (i.e. Ly = b, Ux = y).
c) Compute the determinant of A two ways, first by the usual method and second by the formula |A| = a111a222a333 , where ani denotes the pivot element in step i of Gaussian elimination.
Explanation / Answer
A*X = B