MATH311 practice1

MATH311 practice1 - Math 311 first practice exam...

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Unformatted text preview: Math 311 first practice exam Instructions: This is a closed-book exam. You have 50 minutes. Use the backs of the pages for scratch paper; if you attach more pages, write your name on every extra page you use. Make sure to show all your work, and provide clear details. Each problem is worth 10 points. 1. Does the line 1 0 x=s 0 intersect the plane 2 0 -6 x = t 1 + u 3 + 0 0 1 1 3 in R ? If it does, find their point of intersection. 2. Find the inverse of the matrix 2 4 8 1 0 0 . 1 -3 -7 2 -1 1 0 3 1 . 2 -2 1 3. Find the determinant of the matrix 4. Let 1 0 1 2 3 and B = 0 1 2 . A = 2 1 2 3 0 0 1 Calculate each of the following quantities, or state that it does not exist: (a) AB, (b) BA, (c) A2 , (d) B 2 . 5. Show that the system's solutions form a 2-plane, and find that plane: x 1 1 2 0 y = 0. 1 2 4 -1 z w 6. Let A be some n n matrix such that the equation Ax = 0 has more than one solution. Let B be any n n matrix. Show that the equation BAx = 0 also has more than one solution. 1 ...
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