5 You are given a matrix A and two vectors b1 and b2 You are

5. You are given a matrix A and two vectors b1 and b2. You are tasked with computing the solution to Ax1 = b1 and Ax2 = b2. Would you use Gaussian elimination or LU decomposition? Justify.

Solution

To solve system of equations of the form Ax = b, we use Gaussian elimination. LU decomposition will be the preferred method when we expect to do multiple calculations for different values of vector b.

In LU decomposition, once the matrix has been decomposed into LU form, we can readily use it in future in case the vector b changes.