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

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
In i, Trace M = 0 . 8 and det M = 0, so the eigenvalues must be 0.8 and 0. The corre-
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern