BIOL 205 Midterm: BIOL 205 UNC 2006 Exam IV Solutions
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Math 2418 linear algebra exam #2 part a. An orthonormal basis for the column space of a is. Let w = span{1 + t, 1 3t}. Note that {1 + t, 1 3t} is an orthogonal set. Using the inner product < f, g >= r 1. 1 f (t)g(t)dt, < 1 + t, 1 + t >= 8. 3 and < 1 3t, 1 3t >= 8. A vector in the orthogonal complement of w is. Find an orthogonal basis for span{1 + t, 1 3t, 7t5} which includes 1 + t and 1 3t. Math 2418 linear algebra exam #2 part b. The following matrix has only one eigenvalue: a = Find the eigenvalue and a basis for the eigenspace corresponding to this eigenvalue. List 3 eigenvectors of a corresponding to : List two vectors in r3 which are not eigenvectors of a: Let < (u1, u2), (v1, v2) > = 4u1v1 + 2u1v1.
