MATH 0520 Midterm: MATH 052 Brown Midterm2alternate

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turquoisegnu128

31 Jan 2019

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Suppose a 1v1 = e1, a 1v2 = e2, and a 1v3 = e3, where v1 = (note: e1e2, e3 denote the standard basis vectors in r3. ) Consider the linear transformation s(cid:18)(cid:20) x y (cid:21)(cid:19) = (cid:20) 3x. De ne t to be the 135-degree counterclockwise rotation in r2. Find the determinant of the composition s t. explain your reasoning. Show that det(ka) = kn det a, if k is a real number and a is an n n matrix. Find a basis for the row space of a and a basis for the column space of a. Find the rank and the nullity of a. Consider the set s = { f (x) = 0 for some x [0, 1]} of continuous functions from [0, 1] to r which are zero some- For example, the function (cid:16)x 1 is in s since it vanishes at x = 1.

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Problem 4 Circle your answer. a) (6 points) If f(x) = 2x + 3x2 - 361 + 5, then the tangent line to the graph y= f(x) is horizontal when i) 1 = -2,3 ii) I = 2,-3 iii) r = 0 iv) not listed b) [6 points] Suppose Given h(x) = f(g(T)), where g(2) = 3, g'(2) = 7, f'(2) = -1 and 1'(3) = -2. Then h'(2) is equal to i) - 1 ii) -2 iii) - 14 iv) not listed (x+3)(1 - 1)3 c) (6 points) The function f(1) == (x2 - 2x + 1)(x + 3) wa has vertical asymptotes at i) x = -3,0 ii) = -3,0,1 iii) x = 0,1 iv) not listed d) (6 points] The solution to the initial value problem v'(x) = 473 – cos(x) +e", y(0) = 3 is i) y(x) = x + sin(x) + e* + 2 ii) y(I) = x4 – sin(x) +et+2 iii) y(x) = 2* – sin(1) + et + 3 iv) not listed

need help with question 5, full solutions and work required. thanks

MATH 0520 Midterm: MATH 052 Brown Midterm2alternate

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