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Linear Algebra

Worksheet 16

  1. Find the QR factorization for \(A = \begin{pmatrix} 1 & -1 & -3 \\ 0 & 1 & -1 \\ 1 & 1 & 1 \end{pmatrix}\)

  2. Find the QR factorization for \(A = \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{pmatrix}\)

  3. Assume we start with a linearly dependent set $v_1,\ldots,v_d$ and apply Gram-Schmidt. What happens?