MATH 232 Final: MATH232 MATH232 FinalA

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For this question, you will only be graded on your answer, so you don"t need to justify your answer or show all your calculations. [2] (a) find the point(s) of intersection, if any, of the two lines x = s + 1, y = 3 2s, z = 1. 2 s + 2 and x = t 1, y = t 5, z = 7 t in r3. (b) the 4 7 matrix b has rank 3. How many zero rows does any row echelon form of. B have? (c) for what value(s) of k is the set b = nh 1. 0 (d) find the dominant eigenvalue of the matrix h 6 0. 0 4 7i, if it has one. (e) the matrix (cid:2) 1 2. 1(cid:3) has eigenvalue 1 = 1 + 2i with corresponding eigenvector (cid:2) i. Find an eigenvector corresponding to the conjugate eigenvalue 2 = 1 2i.

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