linalg040April2007 - Linear Algebra 040b Final Examination...

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

View Full Document Right Arrow Icon
Linear Algebra 040b Final Examination Saturday, April 14, 2007 1. [ 2 marks ] Let θ be the angle between the vectors (1 , - 2 , 3) and (3 , 3 , 1). Find cos( θ ). 2. [ 4 marks ] Let be the line in R 3 passing through the points (2 , 4 , 1) and (4 , 0 , 7). (a) Find parametric equations for . (b) Find the point of intersection of with the xy -plane. 3. [ 8 marks ] Find (if possible) the conditions on a, b and c for which the following system of equations has no solution, one solution and infinitely many solutions. x - y + 3 z = a y + z = b x + 4 z = c (Note: you do not have to find actual solutions.) 4. [ 8 marks ] Let W = Span( S ) where S = 1 2 0 1 , 2 3 1 3 , 0 1 2 2 , 1 4 1 2 . Find a subset of S which is a basis of W . 5. The characteristic polynomial of the matrix A = 0 - 2 - 3 1 3 3 0 0 1 is given by p ( λ ) = ( λ - 1) 2 ( λ - 2) .
Image of page 1

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

View Full Document Right Arrow Icon
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