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mat67-Homework5

# mat67-Homework5 - MAT067 University of California Davis...

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MAT067 University of California, Davis Winter 2007 Homework Set 5: Exercises on Matrices and Linear Maps Directions : Please work on all problems! Hand in solutions to the Calculational Problems 1, 2(i,m,r), 5(a), 6(a) and the Proof-Writing Problems 11 and 13 at the beginning of lecture on February 9, 2007. As usual, we are using F to denote either R or C . 1. Suppose that A , B , C , D , and E are matrices over F having the following sizes: A is 4 × 5 , B is 4 × 5 , C is 5 × 2 , D is 4 × 2 , E is 5 × 4 . Determine whether the following matrix expressions are defined, and, for those that are defined, determine the size of the resulting matrix. (a) BA (b) AC + D (c) AE + B (d) AB + B (e) E ( A + B ) (f) E ( AC ) 2. Suppose that A , B , C , D , and E are the following matrices: A = 3 0 1 2 1 1 , B = bracketleftbigg 4 1 0 2 bracketrightbigg , C = bracketleftbigg 1 4 2 3 1 5 bracketrightbigg , D = 1 5 2 1 0 1 3 2 4 , E = 6 1 3 1 1 2 4 1 3 . Determine whether the following matrix expressions are defined, and, for those that are defined, compute the resulting matrix. (a) D + E (b) D E (c) 5 A (d) 7 C (e) 2 B C (f) 2 E 2 D (g) 3( D + 2 E ) (h) A A (i) AB (j) BA (k) (3 E ) D (l) ( AB ) C (m) A ( BC ) (n) (4 B ) C + 2 B (o) D

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