MATH 240 Midterm: MATH240 spring2007M1 math232
31 Jan 2019
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No credit will be given for just writing down the answer: if the answer space provided is not su cient, write your answer on the back of the previous page. Clearly mark the question number: the last question is a bonus question. This question receives no partial credit: all the best. 3: consider the matrix (a) (3 points) compute det(a). Page 3 of 11: consider the matrix. A = ( 10 12 (a) (3 points) compute the characteristic polynomial of a. Answer (b) (4 points) compute the eigenvalues of a and the corresponding eigenspaces. Answer (c) (2 points) give an invertible matrix p and a diagonal matrix d such that a = p 1dp . Page 4 of 11: let w r3 be the subspace spanned by { . 0 (a) (3 points) compute a basis for w . Answer (b) (3 points) compute the orthogonal projection of your method.
