Hw1 - STAT424 Spring 2010 Homework#1 Homework 1 Due Tuesday Feb 2 2010 1 Questions involve the following matrices 1100 12 1 1 0 0 1 2 A= 0 1 1 1;B

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STAT424 Spring 2010 Homework #1 Jan 26, 2010 Homework 1 Due: Tuesday, Feb 2, 2010 1) Questions involve the following matrices: A = 1 1 0 0 1 1 0 0 0 1 1 1 0 1 0 1 ; B = 1 2 0 1 2 0 0 1 0 0 1 1 ; D = 1 2 1 2 2 5 0 0 ; E = 1 0 1 0 3 0 0 2 . (a) Which of the matrices have linearly independent columns? (b) Which of the following equalities are valid: C ( A ) = C ( B ), C ( A ) = C ( A,D ), C ( A,B ) = C ( D,E )? (c) Give the ranks of the matrices. (d) Give an orthonormal basis for C ( A ). (e) Find C ( A ) and C ( D ) (with respect to R 4 ). 2) Write the following models in matrix notation and find the dimension of C ( X ). (a) One-way ANOVA model y ij = μ + α i + ± ij , where i = 1 : 3, and j = 1 : 2 when i = 1 , 2 and j = 1 : 3 when i = 3. (b) Same as (a) but with a constraint that α 1 = α 2 . (c) Same as (a) but with a consraint that
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This note was uploaded on 10/24/2010 for the course STAT 424 taught by Professor Liang,f during the Spring '08 term at University of Illinois, Urbana Champaign.

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Hw1 - STAT424 Spring 2010 Homework#1 Homework 1 Due Tuesday Feb 2 2010 1 Questions involve the following matrices 1100 12 1 1 0 0 1 2 A= 0 1 1 1;B

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