combinepdf-min-0323.pdf - Notes on linear algebra(Monday...

This preview shows page 1 out of 1 page.

Image of page 1
You've reached the end of this preview.

Unformatted text preview: Notes on linear algebra (Monday 17th October, 2016, 23:10) page 170 o a nonzero row of A cannot follow a zero row of A, and o the first nonzero entry in each nonzero row of A is strictly further right than that in the row before. Here are some first simple observations: Proposition 3.151. Let A be an a x m-matrix. Assume that A is a row-echelon matrix. Let k be the number of nonzero rows of A. (a) The first k rows of A are nonzero, whereas the last a — k rows of A are zero. (b) The pivot cells of A are the k cells (1, pivind (row1 A)) , (2, pivind (rowz A)) , . . . , (k, pivind (row,C A)) . (c) We have pivind (rowl A) < pivind (rowz A) < - - - < pivind (rowk A) . Proof of Proposition 3.151. The matrix A is a row-echelon matrix. Thus, the condi- tion in Definition 3.149 shows that, for each i 6 {1,2, . . .,a m 1}, the following holds: if raw.- . 1 A is. nnnzern- then row; A is. nnnzprn. {143) ...
View Full 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