Solve the Equation Ax = B by Using the LU

question 26

Multiple Choice

Solve the equation Ax = b by using the LU factorization given for A.
- $$A = \left[ \begin{array} { r r r r } 1 & 2 & 4 & 3 \\- 1 & - 3 & - 1 & - 4 \\2 & 1 & 19 & 3 \\1 & 5 & - 9 & 7\end{array} \right] , \mathbf { b } = \left[ \begin{array} { l } 2 \\0 \\4 \\3\end{array} \right]$$
$$A = \left[ \begin{array} { r r r r } 1 & 0 & 0 & 0 \\- 1 & 1 & 0 & 0 \\2 & 3 & 1 & 0 \\1 & - 3 & - 2 & 1\end{array} \right] \left[ \begin{array} { r r r r } 1 & 2 & 4 & 3 \\0 & - 1 & 3 & - 1 \\0 & 0 & 2 & 0 \\0 & 0 & 0 & 1\end{array} \right]$$

• A) \(\mathbf { x } = \left[ \begin{array} { r } 27 \\ 9 \\ 8 \\ - 3 \end{array} \right]\)
• B) \(\mathbf { x } = \left[ \begin{array} { r } 27 \\ - 18 \\ 89 \\ - 13 \end{array} \right]\)
• C) \(\mathbf { x } = \left[ \begin{array} { c } 41 \\ - 6 \\ - 3 \\ - 5 \end{array} \right]\)
• D) \(\mathbf { x } = \left[ \begin{array} { r } 2 \\ - 2 \\ 8 \\ - 3 \end{array} \right]\)