MATH 310 Midterm: Math 310 Exam 2
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This is a version of an old exam replacing some topics we didn"t cover yet. Solutions will be posted over the weekend: consider the matrix a = (cid:20)3 2. 1 (a) what are the eigenvalues of a? (b) what are the eigenvectors of a? (c) find a diagonalization of the matrix a. (d) compute the matrix a5: the matrix b has reduced echelon form u , where. 0 (a) give a basis for row b. What is the dimension? (b) give a basis for col b. What is the dimension? (c) give a basis for nul b. What is the dimension? (d) for what values of a and b does the matrix. 0 0 0 b 2 have rank 2: let e = (cid:26)(cid:20)1. 1(cid:21)(cid:27) be the standard basis for r2. (a) show that b = (cid:26)(cid:20)2. 1(cid:21)(cid:27) is another basis for r2. (b) write down the change of basis matrix p.
