MATH V2010 Final: MATH V2010 Columbia S11Final LinearAlgebra S11
31 Jan 2019
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[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.
