MATH V2010 Columbia S11Exam2 LinearAlgebra S11

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Published on 31 Jan 2019
School
Columbia University
Department
Mathematics
Course
MATH V2010
Professor
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
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[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
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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.