MATH 142 Midterm: MATH 142 South Carolina Test2 sample
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If needed, use the back or the next empty page for work. If you need additional paper, write your name on it: do not detach pages from this exam packet or un-staple the packet, please write neatly. Answers which are illegible for the grader can not be given credit: no notes, books, calculators, computers, or other electronic aids can be allowed, you have 90 minutes time to complete your work. If x is the least squares solution of ax = b, then. This is pythagoras applied to the orthogonal vectors b ax , ax . Solution: det(s 1as) = det(s 1)det(a)det(s) = det(a). If is an eigenvalue of a, then 3 is an eigenvalue of a3. A shear in the plane is not diagonalizable. Indeed, the shear in the plane is the prototype of a nondiagonalizable transformation. If a is invertible, then a and a 1 have the same eigenvectors.
