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Exercises 11.5 Homework

1.

(Theoretical problem.) Find a matrix \(A\) of rank 1 such that

\begin{equation*} A \begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix} = \begin{pmatrix} 3 \\ 1 \\ 5 \end{pmatrix} \end{equation*}
2.

Use Broyden's method to solve the nonlinear system

\begin{equation*} \begin{cases} x^2 + y^2 +\sin(x+y) \amp = a \\ x+y+\cos(xy) \amp = 5 \end{cases} \end{equation*}

where \(a\) is the number formed by the first two digits of your SUID.

Try at least two different starting points (or more, if needed to find a solution). Report the outcome of running the method for each starting point. Was the root you found always the same?