# solutions7ac - Math 33b Quiz 7ac Name UCLA ID Consider the...

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Math 33b, Quiz 7ac, March 11, 2008 Name: UCLA ID: Consider the system of differential equations x ( t ) = M x , where M is each of the matrices below. For each system of differential equations, a sample solution in the x - y plane is plotted below. Below each matrix, write the letter of the corresponding graph. (You need not show your work.) Do not assign more than one graph to a matrix or vice-versa. i. parenleftbigg 0 . 6 - 0 . 4 - 0 . 3 0 . 2 parenrightbigg . ii. parenleftbigg 0 . 4 0 . 1 0 . 1 0 . 4 parenrightbigg . iii. parenleftbigg 0 . 1 0 . 5 - 0 . 2 0 . 1 parenrightbigg . iv. parenleftbigg 0 . 3 0 . 4 - 0 . 2 - 0 . 6 parenrightbigg . (Note that in the actual quiz which was handed out in section, arrows were hand-draws on each of the graphs. In A and B, the arrows point to the right. In C and D, they point away from the origin.) -4 -3 -2 -1 1 2 3 4 -4 -3 -2 -1 1 2 3 4 A -4 -3 -2 -1 1 2 3 4 -4 -3 -2 -1 1 2 3 4 B -4 -3 -2 -1 1 2 3 4 -4 -3 -2 -1 1 2 3 4 C -4 -3 -2 -1 1 2 3 4 -4 -3 -2 -1 1 2 3 4 D Solution. i-A, ii-C, iii-D, iv-B. 1

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In i, Trace M = 0 . 8 and det M = 0, so the eigenvalues must be 0.8 and 0. The corre-
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