Let A+ be defined as in Exercise 10 and let P = AA+. Show that P2 =

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Let A+ be defined as in Exercise 10 and let P = AA+. Show that P2 = P and PT = P.
Exercise 10
Let A be an m × n matrix of rank n with singular value decomposition Uˆ‘VT. Let ˆ‘+ denote the n × m matrix
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and define A+ = Vˆ‘+ UT. Show that = A+b satisfies the normal equations ATAx = ATb.

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