Homework 3 (due 2-15) - CSE 3380 Homework#3 Assigned Due...

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CSE 3380 – Homework #3 Assigned: Monday, February 8, 2016 Due: Monday, February 15, 2016 at 3:50pm (the end of class) Note the following about the homework: 1. You must show your work to receive credit. 2. If your submission has more than one page, staple the pages. Assignment: Process 1. For each set of partitioned matrices below, find AB using multiplication of partitioned ma- trices. The partitions to use are given. a ) A = 1 2 3 4 5 6 7 8 0 1 0 2 3 0 4 0 , B = 1 2 3 4 1 3 2 4 , b ) A = 1 2 3 4 5 6 7 8 0 1 0 2 3 0 4 0 , B = 1 2 3 4 1 3 2 4 2. Find the determinants of the following: a ) A = bracketleftbigg 1 3 - 2 - 6 bracketrightbigg , b ) A = 1 2 0 3 0 1 0 1 4 , c ) A = 1 0 0 0 2 0 0 3 0 0 0 4 0 0 0 0 0 0 0 5 0 0 0 6 0 , d ) A = 1 2 3 4 5 0 1 6 6 - 3 0 0 1 9 10 - 2 - 4 - 6 - 7 1 0 3 18 18 - 8 Theory For each of the following, use the rules of matrix algebra to show that the relationship is true. Don’t replace the matrices by matrices with actual numbers nor generic matrices in which you use dot products to perform the multiplication. You should be able to show these using the representation of a matrix by a single letter, which is one of the strengths of the matrix representation of the relationships between values. 3. If A,B R n × n , show that A ( B - 1 ( A + B ) A - 1 ) B = A + B 4. If A R m × n , B R n × p , C R p × q , and D R q × t , show that ( ABCD ) T = D T C T B T A T
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  • Spring '16
  • Darin Brezeale
  • Geometry, Trigraph, ax ay, dx dy d2, ax ay a2x, cx cy

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