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Unformatted text preview: 1. Linear Algebra Problems 1. (too easy) Find the linear combination 3 a 1 + 5 a 2 a 3 of the vectors a 1 = < 4 , 3 , 1 , 2 >, a 2 = < 1 , 2 , 3 , 2 >, a 3 = < 16 , 9 , 1 , 3 > . 2. (too easy) Find the vector bfx from the equation a 1 + a 2 + 3 a 3 + 4 x = 0 where a 1 = < 5 , 8 , 1 , 2 >, a 2 = < 2 , 1 , 4 , 3 >, a 3 = < 3 , 2 , 5 , 4 > . 3. (easy) Are the vectors below linearly independent? a 1 = < 4 , 2 , 6 >, a 2 = < 6 , 3 , 9 > ; 4. (easy) Find a basis of the system of vectors below, and express the rest of the vectors in that basis. a 1 = < 2 , 1 >, a 2 = < 3 , 2 >, a 3 = < 1 , 1 >, a 4 = < 2 , 3 > ; 5. When does a system of vectors have a unique basis? 6. Find the general solution, and a particular solution of the system below using the Gauss elimination metod. 5 x 1 + 3 x 2 + 5 x 3 + 12 x 4 = 10 2 x 1 + 2 x 2 + 3 x 3 + 5 x 4 = 4 x 1 + 7 x 2 + 9 x 3 + 4 x 4 = 2 . 7. (precalcish, but...) Find a degree two polynomial with real coefficients, f ( x ) , such that f (1) = 8...
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This note was uploaded on 01/18/2012 for the course INFORMATIK 2011 taught by Professor Phanthuongcang during the Winter '11 term at Cornell University (Engineering School).
 Winter '11
 PhanThuongCang

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