260S0708M1Sol - Instructor Time Duration Signature Last...

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Unformatted text preview: Instructor Time Duration Signature : : : : : : Last Name Name ID Number M E T U Department of Mathematics Math 260 Basic Linear Algebra Exam 1 18.07.2008 13: 00 90 minutes 5 QUESTIONS ON 4 PAGES TOTAL 30 POINTS ANSWER KEY 1 2 3 4 5 (1) (2+3+1=6 pts.) The nodal incidence matrix M of a directed graph consisting of vertices V 1 ,V 2 ,...,V m and edges E 1 ,E 2 ,...,E n is defined by M ij =      1 if E j leaves V i- 1 if E j enters V i if E j and V i are not connected . (a) Find the nodal incidence matrices A , B and C of the following graphs: V V V E E 1 1 2 2 3 V V E E E 1 1 2 2 3 V V V E E E 1 1 2 2 3 3 A =    1 1- 1- 1    B = " 1- 1 0- 1 1 0 # C =    1- 1- 1 1 1- 1    (b) Find the matrix A · B + C A · B + C =    0 0- 1 1 0 1- 1 0    +    1- 1- 1 1 1- 1    =    1- 1- 2 1 1 1- 1    (c) Why does the expression A · C + B make no sense?...
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260S0708M1Sol - Instructor Time Duration Signature Last...

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