Exam 2

Linear Algebra, Dave Bayer, March 29, 2011

Name:

[1] (5 pts) [2] (5 pts) [3] (5 pts) [4] (5 pts) [5] (5 pts) [6] (5 pts) TOTAL

Please work only one problem per page, starting with the pages provided. Clearly label your

answer. If a problem continues on a new page, clearly state this fact on both the old and the new

pages.

[1] Find a basis for the rowspace of the following matrix. Extend this basis to a basis for all of R4.

3 2 1 0

1 1 1 1

0 1 2 3

[2] Find the determinant of each of the following matrices.

1 2 3 4

0 3 4 5

0 0 1 3

0 0 2 9

a b c d

a b +1c d

a b c +1d

a b c d +1

1 2 3 4

1 4 3 4

1 2 6 4

1 2 3 8

## Document Summary

[1] (5 pts) [2] (5 pts) [3] (5 pts) [4] (5 pts) [5] (5 pts) [6] (5 pts) total. Please work only one problem per page, starting with the pages provided. If a problem continues on a new page, clearly state this fact on both the old and the new pages. [1] find a basis for the rowspace of the following matrix. Extend this basis to a basis for all of r4. [2] find the determinant of each of the following matrices. 0 0 2 9 b a a b + 1 a a b b c c c + 1 d d d c d + 1. [3] find the inverse of the following matrix. [4] let v1 = (1,0,0), v2 = (1,1,0), v3 = (0,1,1) R3 be a linear map such that. Find the matrix a (in standard coordinates) which represents the linear map l.