MATH-205 Midterm: Bates MATH 205 041012webster205exam
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You must show all work to receive credit. No electronic devices other than calculators are permitted. Give exact answers (such as ln 5 or e2) unless requested otherwise: let ~v1 = Explain. (c) let w = span{~v1, ~v2, ~v3}. Find an orthogonal basis for w : recall the di erence between 4 and solving x2 = 4. The former is 2 while the latter has the solutions x = 2 or x = 2. We call that positive root of x2 4 = 0 the principal root of 4 and write 4. By diagonalizing a matrix and taking the square roots of the eigenvalues, we may compute the square root of a matrix. (a) let a = (cid:20) 9 15. Compute a. (b) write all solutions to x2 = a. (c) suppose a was a 3 3 matrix with 3 positive, distinct eigenvalues.
