hw5.pdf - Linear Algebra Fall 2018 HW#5 Please give complete well-written solutions to the following exercises Show all work to relieve full credit

hw5.pdf - Linear Algebra Fall 2018 HW#5 Please give...

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

Linear Algebra - Fall 2018 HW #5 Please give complete, well-written solutions to the following exercises. Show all work to relieve full credit! Total number of points: 65 (+10 extra credit) I adapted the shape of the homework sheet a bit for them to be a better preparation for the second midterm and final. (1) (3 points (0.5 each)) Fill in the blanks (a) Let A be a 10 × 7 matrix with rank 5. Then the dimension of C ( A ) is and the dimension of C ( A T ) is . (b) The nullspace N ( A ) and the row space C ( A T ) are subspaces of R n . Every vector x N ( A ) is perpendicular to every of A . (c) Let a 1 , . . . , a n be independent vectors in R m and let b R m . The projection p of b onto the subspace spanned by a 1 , . . . , a n is given by p = . It is the vector in that subspace that is to b . (2) (9 points) Let A = 1 2 3 4 5 6 7 8 9 . a) (3 points) Determine a basis of the nullspace N ( A ). b) (2 points)Find the dimensions of the four subspaces N ( A ) , C ( A ) , C ( A T ) and N ( A T ).
Image of page 1

Subscribe to view the full document.

Image of page 2
  • Spring '14
  • Li
  • Linear Algebra, Total Number of points, row space C

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 0 bonus questions You can ask 0 questions (0 expire soon) You can ask 0 questions (will expire )
Answers in as fast as 15 minutes