MATH 308 Final: Final Exam
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2: (10 points) find the value(s) of x which makes the following matrix non-invertible: 3. (a) (5 points) suppose we have two vectors ~u1 and ~u2 in r675981110111 such that ||~u1|| = 3, ||~u2|| = 4 and ~u1 ~u2 = 1. Find ||2~u1 + ~u2||. (b) (5 points) suppose we have two orthogonal vectors ~u3 and ~u4 in r10198230535 such that. ||~u4|| = 1 and ||~u3 + ~u4|| = 2. 4. (a) (3 points) let a = (cid:18) 2. 1 (b) (7 points) consider the following linear transformations. Here, a is the 2 2 matrix given in part (a). = (cid:18) y3 y1 + y2 (cid:19) . Find the 2 3 matrix corresponding to a linear transformation u : r3 r2 such that. 5. (a) (3 points) suppose a is a n n matrix with an eigenvector ~u associated to the eigenvalue. And an eigenvector ~v associated to the eigenvalue ( 6= ).
