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Unformatted text preview: b = QQ T b (c) The error vector e = b − p is contained in the left nullspace of Q , the nullspace of Q T . To check this, we compute ⎛ ⎜ Q T e = Q T b − QQ T b = Q T b − Q T QQ T b = Q T b − IQ T b = Question 6. The product P 2 P 1 is projection onto the column space of P 1 , followed by the projection onto the column space of P 2 . Since the column space of P 2 contains the column space of P 1 , the second projection does not change the vectors anymore. Thus ⎞ ⎞ ⎞ − 1 ⎞ 1 1 1 2 1 ⎟ 2 ² ⎟⎛ ⎜ ⎟ 2 ²² ⎛ 2 ² ⎜ 1 ⎟ 2 4 ⎟ ² ⎟ 1 ⎟ ² P 2 P 1 = P 1 = 2 1 ⎟ ²² 1 2 1 = ⎠ ± ⎠ ⎠ ±± 6 ⎠ ± 1 1 1 2 1 2...
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 Spring '05
 Strang
 Linear Algebra, column space, nonzero positive multiple

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