Final Exam

Linear Algebra, Dave Bayer, May 10, 2011

Name:

[1] (5 pts) [2] (5 pts) [3] (5 pts) [4] (5 pts) [5] (5 pts) [6] (5 pts) [7] (5 pts) [8] (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] By least squares, ﬁnd the equation of the form y=ax +bwhich best ﬁts the data

x1y1

x2y2

x3y3

=

0 1

1 1

3 2

[2] Extend the vector (1,1,1,2)to an orthogonal basis for R4.

[3] Find the orthogonal projection of the vector (1,0,0,0)onto the subspace of R4spanned by the

vectors (1,1,1,0)and (0,1,1,1).

## Document Summary

[1] (5 pts) [2] (5 pts) [3] (5 pts) [4] (5 pts) [5] (5 pts) [6] (5 pts) [7] (5 pts) [8] (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] by least squares, nd the equation of the form y = ax + b which best ts the data x1 y1 x2 y2 x3 y3. [2] extend the vector (1,1,1,2) to an orthogonal basis for r4. [3] find the orthogonal projection of the vector (1,0,0,0) onto the subspace of r4 spanned by the vectors (1,1,1,0) and (0,1,1,1). [4] find the matrix a which projects r4 orthogonally onto the subspace spanned by the vectors (1,1,1,1) and (1,1,2,2). [5] find the eigenvalues and corresponding eigenvectors of the matrix. [6] find the matrix exponential eat, for the matrix.