hw1sol - Stat 511 Homework 1 solutions( Total pts: 20)...

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Unformatted text preview: Stat 511 Homework 1 solutions( Total pts: 20) Spring 2011 Let A = 1 2 3 0 1 0 , B =- 1 5 2- 1 , and C = 0 1- 1 1 2 1 . 1. C + A = 1 1 5 1 2 1 . 2. BA =- 1 3- 3 2 3 6 . 3. AB is not well defined. 4. tr ( B )=-1+ -1=-2. 5. BAC =- 9- 1 9 11 CBA = 2 3 6 3 0 9 0 9 0 ACB = 8 14 3- 6 By the cyclical property of the trace tr ( BAC ) = tr ( CBA ) = tr ( ACB ) = 2. 6. What is the column rank of the following X X matrix? Rank 1 2 0 0 2 4 0 0 0 0 9 1 0 0 1 4 = 3 Column 2 is 2xColumn 1. None of the other columns can be expressed as a linear combination of the others, so rank is 4-1=3 7. What is the column rank of the following design matrix? Rank 1 1 0 1 0 1 0 0 0 1 1 0 1 0 1 0 0 0 1 1 0 0 1 0 1 0 0 1 1 0 0 1 0 1 0 0 1 0 1 1 0 0 0 1 0 1 0 1 1 0 0 0 1 0 1 0 1 0 1 0 0 0 1 1 0 1 0 1 0 0 0 1 = 4 Column 3 is Column 1 - Column 2, Column 5 is Column 1 - Column 4, Column 7 is Column 2- Column 6, Column 8 is Column 4 - coumn 6, Column 9 is Column 1 - (Column 2 + Column 4 - Column 6). So rank is 9 - 5 = 4....
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hw1sol - Stat 511 Homework 1 solutions( Total pts: 20)...

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