MATH-205 Midterm: Bates MATH 205 111309ross205exam
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In this problem, assume a and b are 4 4 square matrices. Suppose: rref(a)= r where r has exactly three leading-1"s, rref(b)= s and s = i4. 1 2 (i) v = (iii) u = : let b = Here are some facts about b: (ii) = 10 is an eigenvalue of b, 2: find the characteristic polynomial of c in factored form starting from det(c i); show all your work, one of the eigenvalues should have multiplicity 2. Find a basis for the eigenspace of that eigenvalue: without actually nding p , d and p 1, explain why c is diagonalizable. Name: let m be the 4 4 matrix here. 30 (a) use this fact to nd the eigenvalues of m , and bases for their respective eigenspaces. {z not useful information! (b) is m diagonalizable? (y/n) 0 e: let d = (a) det(d3) and suppose det(d)= 10.
