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HW03 - 8 1 − 3 1 ⎞ ⎟ ⎟ ⎟ ⎟ ⎠(b ⎛ ⎜ ⎜...

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EE 203000 Linear Algebra Homework #3 (Due November 27, 2009 BEFORE class) Note: Detailed derivations are required to obtain a full score for each problem. (Total 112%) 1. (6%+6%) Problem 17 of Section 2.4. [Problem 10 of HW#2] 2. (8%) Let T be the linear operator on P 1 ( u1D445 ) defined by T ( u1D45D ( u1D465 )) = 2 u1D45D ( u1D465 ), where u1D45D ( u1D465 ) is the derivative of u1D45D ( u1D465 ). Let u1D6FD = { 1 , u1D465 } and u1D6FD = { 1 u1D465, 1 + u1D465 } . Find [ T ] u1D6FD . 3. (10%) Problem 4 of Section 3.1. (This result implies that the same elementary matrix can be used to perform either an elementary row or an elementary column operation de- pending on which side it is multiplied to the matrix of interest.) 4. (6%+6%) Find the rank and the inverse (if exists) of the following matrices: (a) 1 2 0 1 1 2 4 1 3 0 3 6 2 5 1 4 8 1 3 1
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Unformatted text preview: 8 1 − 3 1 ⎞ ⎟ ⎟ ⎟ ⎟ ⎠ (b) ⎛ ⎜ ⎜ ⎜ ⎜ ⎝ 1 1 1 1 1 − 1 2 2 1 − 1 1 − 3 ⎞ ⎟ ⎟ ⎟ ⎟ ⎠ . 5. (10%) Problem 12 of Section 3.2. 6. (8%+6%+6%) Problem 14 of Section 3.2. 7. (8%+6%) Determine if the following systems of linear equations are consistent and, if so, ±nd the solution set and the null space of L U , where ³ is the coeﬃcient matrix. (a) ± 1 + ± 2 − ± 3 + 2 ± 4 = 1 4 ± 1 + ± 2 − 2 ± 3 + ± 4 = 3 (b) ± 1 + 2 ± 2 − ± 3 = 1 2 ± 1 + ± 2 + 2 ± 3 = 3 ± 1 − 4 ± 2 + 7 ± 3 = 4 . 8. (6%) Problem 2(h) of Section 3.4 9. (8%+4%) Problem 3 of Section 3.4 10. (8%) Problem 8 of Section 3.4. 1...
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