MAT 310 Midterm: MAT 310 SBU Fall12 PMidtermIISolutionsodd

• School: Stony Brook University
• Department: Mathematics
• Course: MAT 310
• Professor: All

Document Summary

Solution 0. 1 (problem 1) label the left and right vertices l, r make an adja- cency matrix, a, with columns a, b, l, r: 177: thus the number of paths from a to b of length 4 is 136, the number of loops is the trace of a4 = 4 177 = 400 + 280 + 28 = 708. Note that in class we oriented all edges. Solution 0. 2 (problem 3: the rank is the same as the dimension of the span of the column vectors. the rst three columns, counting from the right are linearly independent so: rank 3. On the other hand, the leftmost column vector is a linear combination of the middle two so: Thus, rank 3 rank = 3: from the last part of this question, we know on the two given vectors. Solution 0. 3 (problem 5) let"s do this by cofactor expansion along the rst column: (1) .