tst1sltn.pdf - MAT343 Section 1 Fall 2014 TEST 1 SOLUTIONS Name(BLOCK LETTERS PLEASE Do NOT write your answers on this sheet please Scale 30 A 25 B 20

tst1sltn.pdf - MAT343 Section 1 Fall 2014 TEST 1 SOLUTIONS...

This preview shows page 1 - 2 out of 3 pages.

MAT343, Section 1, Fall 2014 TEST 1 - SOLUTIONS Name: (BLOCK LETTERS PLEASE!) Do NOT write your answers on this sheet please! Scale: 30 : A 25 : B 20 : C (15A,18B,18C out of 64) Problem 1: Compute the intersection of the three planes in R 3 , given by the equations x - 2 y + z = 0 , 2 x - y - z = 1 , x - 5 y + 4 z = - 1 . Describe the their relative location to each other (i.e. do they intersect, are they parallel?). SOLUTION: First, no two planes are parallel, since no two rows are multiples of each other. We try to compute the intersection: 1 - 2 1 0 2 - 1 - 1 1 1 - 5 4 - 1 Gaussian elimination: R 2 = R 2 - 2 R 1 , R 3 = R 3 - R 1 , R 3 = R 3 + R 2 gives 1 - 2 1 0 0 3 - 3 1 0 0 0 0 So, the rank is 2. there is a one parameter family of solutions. They intersect in a line. Problem 2: For what values of a are the vectors v 1 = 1 0 0 1 , v 2 = 4 1 2 0 , v 3 = 0 0 1 2 , v 4 = 2 a 3 0 linearly dependent in R 4 ?
Image of page 1

Subscribe to view the full document.

Image of page 2

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

Ask Expert Tutors You can ask bonus questions You can ask questions ( expire soon) You can ask questions (will expire )
Answers in as fast as 15 minutes