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1.2 Vector Spaces - 1.2 1.2 Vector Spaces 1(a T(b F(If 0...

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1.2. 1.2. Vector Spaces 1 . (a) T (b) F (If 0 0 s.t. x + 0 0 = x, x V, then 0 0 = 0 + 0 0 = 0 0 + 0 = 0 , 0 0 = 0) (c) F (If x = 0 , a 6 = b , then a · 0 = b · 0 but a 6 = b ) (d) F (If a = 0 , x 6 = y , then a · x = 0 = a · y but x 6 = y ) (e) T (f) F (An m × n matrix has m rows and n cilumns) (g) F (h) F (If f ( x ) = ax + b, g ( x ) = - ax + b , then deg f =deg g =1, deg( f + g )=0) (i) T (p.10 Example4) (j) T (k) T (p.9 Example3) 2 . 0 0 0 0 0 0 0 0 0 0 0 0 3 . M 13 = 3 , M 21 = 4 , M 22 = 5 4 . (a) 6 3 2 - 4 3 9 3 PNU-MATH
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1.2. (b) 1 - 1 3 - 5 3 8 (c) 8 20 - 12 4 0 28 (d) 30 - 20 - 15 10 - 5 40 (e) 2 x 4 + x 3 + 2 x 2 - 2 x + 10 (f) - x 3 + 7 x 2 + 16 (g) 10 x 7 - 30 x 4 + 40 x 2 - 15 x (h) 3 x 5 - 6 x 3 + 12 x + 6 5 . U = 8 3 1 3 0 0 3 0 0 , D = 9 1 4 3 0 0 1 1 0 , T = 17 4 5 6 0 0 4 1 0 ( * ) The total number of crossings Fall Spring Winter Brook trout 17 4 5 Rainbow trout 6 0 0 Brown trout 4 1 0 6 . M = 4 2 1 3 5 1 1 4 3 1 2 6 , 2 M - A = 3 1 1 4 4 0 1 3 5 2 1 9 35 suites were sold during the June sale 4 PNU-MATH
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1.2. 7 . We are going to show that f ( t ) = g ( t ) and ( f + g )( t ) = h ( t ) , t S = { 0 , 1 } (i) f (0) = 1 = g (0) , f (1) = 3 = g (1) (ii) ( f + g )(0) = 2 = h (0) , ( f + g
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