MATH-0070 Final: MATH70 final Math70-Final-Fall07
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No books, notes, or calculators are allowed on the exam. With your signature, you are pledging that you have neither given nor received help in this exam: (10 points) let a = . The eigenvalues of a are 1 and 2. Find an orthogonal matrix u such that u t au is diagonal: (8 points) apply the gram-schmidt process to the following set of vectors: And let w = span {u1, u2}. How can you see this without calculating a determinant or row reducing? (e) find the unit vector in the direction of u1: (5 points) let a = (cid:18) 1 2. 1: (5 points) fill in the blanks: let f (x) = (x 1)m1 (x d)md be the characteristic polynomial of a matrix a. Then a is diagonalizable if for each i = 1, 2, . , d, the dimension of equals: (12 points) let b = {v1, v2} be an ordered basis of a vector space v .
