{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

1.2 Vector Spaces

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

This preview shows pages 1–4. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}