Exercise3

In the following exercises, use the given \(LU\) factorizations to solve the equations \(A\xvec = \bvec\text{.}\)

  1. Solve the equation

    \begin{equation*} A\xvec = \left[\begin{array}{rr} 1 \amp 0 \\ -2 \amp 1 \\ \end{array}\right] \left[\begin{array}{rr} 3 \amp 1 \\ 0 \amp -2 \\ \end{array}\right]\xvec = \twovec{-3}{0}\text{.} \end{equation*}
  2. Solve the equation

    \begin{equation*} A\xvec = \left[\begin{array}{rrr} 1 \amp 0 \amp 0 \\ -2 \amp 1 \amp 0 \\ -1 \amp 2 \amp 1 \\ \end{array}\right] \left[\begin{array}{rrr} 2 \amp 1 \amp 0 \\ 0 \amp -1 \amp 3 \\ 0 \amp 0 \amp 1 \\ \end{array}\right]\xvec = \threevec{5}{-5}{7}\text{.} \end{equation*}
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