| course |
course_year |
question_number |
tags |
title |
year |
Numerical Analysis |
IB |
59 |
IB |
2018 |
Numerical Analysis |
|
Paper 4 , Section I, D |
2018 |
$$A=\left[\begin{array}{cccc}
1 & 2 & 1 & 2 \\
2 & 5 & 5 & 6 \\
1 & 5 & 13 & 14 \\
2 & 6 & 14 & \lambda
\end{array}\right], \quad b=\left[\begin{array}{l}
1 \\
3 \\
7 \\
\mu
\end{array}\right]$$
where $\lambda$ and $\mu$ are real parameters. Find the $L U$ factorisation of the matrix $A$. For what values of $\lambda$ does the equation $A x=b$ have a unique solution for $x$ ?
For $\lambda=20$, use the $L U$ decomposition with forward and backward substitution to determine a value for $\mu$ for which a solution to $A x=b$ exists. Find the most general solution to the equation in this case.