{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

midterm-1-solns

midterm-1-solns - Math 33A Spring 2008 First mid-term exam...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 33A Spring 2008 First mid-term exam Name: Student ID: Instructions. There are five problems, each of which is worth 10 points. Answer each question. For full credit, show all work. Books, electronic devices, and notes may not be used. A piece of scratch paper is attached to the end of the exam. Problem Score 1 2 3 4 5 Total
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
First mid-term exam 2 1. (10 points) Consider the following system of linear equations: y + 2 z = 1 2 x - y - 2 z = 7 x + y + 2 z = 5 . Perform Gauss-Jordan elimination on this system. If the system has any solutions, find all of them, and describe the solution set geometrically. If the system has no solution, state this. Solution: We form the augmented matrix A = 0 1 2 1 2 - 1 - 2 7 1 1 2 5 , and then perform the following row operations: 0 1 2 1 2 - 1 - 2 7 1 1 2 5 I III = 1 1 2 5 2 - 1 - 2 7 0 1 2 1 II - 2 I = 1 1 2 5 0 - 3 - 6 - 3 0 1 2 1 II ÷ - 3 = 1 1 2 5 0 1 2 1 0 1 2 1 I - II, III - II = 1 0 0 4 0 1 2 1 0 0 0 0 So x = 4, y + 2 z = 1. For a real parameter t , we set the free variable z = t , and see that there are infinitely
Image of page 2
Image of page 3
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