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# hw5 - Home Work 5 Due May 5 2008 Three pages All sections...

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Home Work 5 Due May 5, 2008 Three pages All sections covered in home work assignments (including this one) are included for the mid-term on May 7th. The best way to prepare is to go through the problems at the back of each section. Note : If you are having difficulties with these problems make sure you bring them up in your discussion sessions. 1. (a) Write the 6x4 incidence matrix A for the graph in Figure 1. The y 1 y 2 y 4 y 5 y 6 x 4 x 1 x 2 y 3 x 3 Figure 1: For problem 1. vector (1,1,1,1) is in the nullspace of A, but now there will be m - n + 1 = 3 independent vectors that satisfy A T y = 0. Find the three vectors y and connect them to the loops in the graph. (b) Write down the dimensions of the four fundamental subspaces for the incidence matrix A from the previous problem, and a basis for each subspace. 2. Every straight line remains straight after a linear transformation. If z is halfway between x and y , show that Az is halfway between Ax and Ay .

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