MATH 1210 Final: MATH 1210 Fall2009FinalExam
31 Jan 2019
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December 2009 final exam: prove using induction that ( 1)r = ( 1)n 1. 1z2: given l1 : hx, y, zi = h7, 1, 4i + sh1, 1, 3i and l2 : hx, y, zi = h3, 2, 0i + th2, 3, 2i. 0 i i (cid:19) find (a) a2 and (b) a 1: find the value of k for which the following system is consistent: 2x + y = 6, x + 3y = 4: find a such that the following vectors are linearly dependent: h 1, 2, ai, h2, 7, 4i, h3, 5, 2ai, let a = . Find: (a) |a| (b) the element in the 2nd row and 3rd column of a 1: let a = . 0 4 (a) find the characteristic equation of a. (b) given that = 1 is one of the eigenvalues, nd the other two: consider the transformation from t : r2 r2 given by.
