Worksheet: QR Decomposition

In this worksheet, we will practice finding the QR decomposition (factorization) of a matrix.

Q1:

Find a QR factoring of the matrix 121321102.

  • A 1 1 1 1 1 3 2 2 6 6 2 6 3 1 1 1 1 5 2 2 6 6 2 6 1 1 1 1 2 2 3 3 2 2 3 1 1 4 1 1 1 1 6 1 1 1 1 0 6 2 2 1 1 2 2 2 1 1 0 0 2
  • B 1 1 1 1 1 3 2 2 6 6 2 6 3 1 1 1 1 5 2 2 6 6 2 6 1 1 1 1 2 2 3 3 2 2 3 1 1 4 1 1 1 1 6 1 1 1 1 0 6 2 2 1 1 2 2 2 1 1 0 0 2
  • C 1 1 1 1 1 3 2 2 6 6 2 6 3 1 1 1 1 5 2 2 6 6 2 6 1 1 1 1 2 2 3 3 2 2 3 1 1 4 1 1 1 1 6 1 1 1 1 0 6 2 2 1 1 2 2 2 1 1 0 0 2
  • D 1 1 1 1 1 3 2 2 6 6 2 6 3 1 1 1 1 5 2 2 6 6 2 6 1 1 1 1 2 2 3 3 2 2 3 1 1 4 1 1 1 1 6 1 1 1 1 0 6 2 2 1 1 2 2 2 1 1 0 0 2
  • E 1 1 1 1 1 3 2 2 6 6 2 6 3 1 1 1 1 5 2 2 6 6 2 6 1 1 1 1 2 2 3 3 2 2 3 1 1 4 1 1 1 1 6 1 1 1 1 0 6 2 2 1 1 2 2 2 1 1 0 0 2

Q2:

Find a QR factoring of the matrix 121030111021.

  • A 1 1 1 1 1 1 0 1 1 0 3 1 1 1 1 3 1 1 0 1 1 0 1 0 1 0 1 1 1 1 1 1 0 1 1 0 3 1 0 1 0 1 1 2 1 1 1 1 6 1 1 1 1 4 1 1 1 1 0 2 1 1 0 1 1 1 1 0 2 2 2 1 1 0 5 5 0 0 1 0 2 1 0 5
  • B 1 1 1 1 1 1 0 1 1 0 3 1 1 1 1 3 1 1 0 1 1 0 1 0 1 0 1 1 1 1 1 1 0 1 1 0 3 1 0 1 0 1 1 2 1 1 1 1 6 1 1 1 1 4 1 1 1 1 0 2 1 1 0 1 1 1 1 0 2 2 2 1 1 0 5 5 0 0 1 0 2 1 0 5
  • C 1 1 1 1 1 1 0 1 1 0 3 1 1 1 1 3 1 1 0 1 1 0 1 0 1 0 1 1 1 1 1 1 0 1 1 0 3 1 0 1 0 1 1 2 1 1 1 3 6 1 1 1 1 4 1 1 1 3 0 2 1 1 0 1 3 1 1 0 2 2 2 1 1 0 5 5 0 0 1 0 2 1 0 5
  • D 1 1 1 1 1 1 0 1 1 0 3 1 1 1 1 3 1 1 0 1 1 0 1 0 1 0 1 1 1 1 1 1 0 1 1 0 3 1 0 1 0 1 1 2 1 1 1 1 6 1 1 1 1 4 1 1 1 1 0 2 1 1 0 1 1 1 1 0 2 2 2 1 1 0 5 5 0 0 1 0 2 1 0 5
  • E 1 1 1 1 1 1 0 1 1 0 3 1 1 1 1 3 1 1 0 1 1 0 1 0 1 0 1 1 1 1 1 1 0 1 1 0 3 1 0 1 0 1 1 2 1 1 1 1 6 1 1 1 1 4 1 1 1 1 0 2 1 1 0 1 1 1 1 0 2 2 2 1 1 0 5 5 0 0 1 0 2 1 0 5

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