hw5_sol_sej

# hw5_sol_sej - EE103 Spring 2010 HW 5 Solution Set Prof S.E...

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EE103 Spring 2010, HW 5 Solution Set, Prof S.E. Jacobsen Page 1 / 5 Applied Numerical Computing Instructor: Prof. S. E. Jacobsen HW5 Solution Set Problem 1. (a) Since P is orthogonal, we have T P P I , and we have PA LU . Then, we have T T T A U L P (1) Then T A y d can be expressed as T T U L Py d (2) Or, we may rewrite (2) as ( ) T T U L Py d We then have , , T T T T z L Py U z d provides z u Py L u z provides u y P u (b) ( ) y rows u . Students, you should generate a small example to see that this result is correct. Problem 2. (a) Since N is orthonormal, N T N = I . Then 2 2 2 2 ( ) ( ) T T T T T Nx Nx Nx x N Nx x Ix x x x , (b) One may observe the L.H.S. of the equation, stated in the question , is 1 2 1 2 1 1 2 2 , , ..., , , ..., ( ... ) T k k T T k kT I q q q q q q I q q q q q q     Since the orthogonality between q i and q j , 1 i , j k , gives q iT q j = 0, the R.H.S., of the equation, stated in the question , is

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