M235A1F08v2 - MATH 235 Linear Algebra II Assignment 1 Due:...

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MATH 235 Linear Algebra II Assignment 1 Due: 9:30 am, Sept. 17/08 in the drop boxes near the tutorial centre. 1. P = 1 3 11 5 0 - 1 - 3 - 2 5 2 16 - 1 Q = 1 3 1 0 2 4 1 1 4 1 1 3 R = 1 1 + i 5 + 3 i 1 + 2 i i - i - i - 3 i - i 0 - 2 i i The entries of matrices P,Q,R are taken from the fields R , Z 5 , and C respectively. For each of the above matrices carry out the following steps: 1. Rename the initial matrix A , with columns a 1 , a 2 , a 3 and a 4 . 2. Find the unique reduced row echelon matrix B , with columns b 1 , b 2 , b 3 , b 4 3. Find a basis for nul A , col A and row A . 4. Is col A = col B ? Why or why not? 5. Write each of b 3 and b 4 as a linear combination of b 1 , and b 2 . 6. Write each of a 3 and a 4 as a linear combination of a 1 , and a 2 . 7. What can you conclude from the results of steps 5) and 6)? 8. Is row A = row B ? Why or why not? 9. Suppose the rows of
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M235A1F08v2 - MATH 235 Linear Algebra II Assignment 1 Due:...

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