Question

Given a nonsingular matrix A € Rn×n and two vectors c, d E R", show how to use the LU factorization with partial pivoting to compute a = = c² A-¹ d. Do not compute any inverse.
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Answer 1

Given:

We have Given a nonsingular matrix A € Rn×n and two vectors c, d E R".

To Find:

We have to show  how to use the LU factorization with partial pivoting to compute a = = c² A-¹ d?

Step-by-step explanation:

• Let a non- singular A belongs to and two vectors c,d belongs to R".

       And now using LU factorization with partial pivoting and

                                 $\alpha =c^T A^-^1d$

• Suppose we are given two matrices L and U such that L is unit lower triangle and U is upper tirangle then

                                   TA=LU

• Solving the system of equation Ax=b where A=LU forward subtitute          Ly=b

          where

                 y(i)=b(i) for i>2

                 y(i)=y(i)-L(i,j)y(j)