MATH-205 Midterm: Bates MATH 205 040908greer205exam
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Your grade is based on correctness, completeness, and clarity on each exercise. You may use a calculator and your single sheet of paper with notes, but may not consult books or other students. Use theorems and concepts from chapter 6 to address the following. Always explain your reasoning thoroughly. a. ) (5 pts. ) Show that the only case in which a vector x can be in both the subspaces w and w is when x = 0. b. ) (5 pts. ) Show that for each vector y and each subspace w , the vector (y projw y) is orthogonal to w . The following questions are all about eigenvalues and eigenvectors. Find the eigenvalues of the matrix a = . Let a be a 3 3 matrix having three distinct eigenvalues. Explain how to diagonalize a. c. ) (5 pts. ) Find a basis for the eigenspace corresponding to the. The following questions are all about linear transformations.
