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1.1 Vector Spaces

# 1.1 Vector Spaces - ⇒ tx = t a 1,a 2 = ta 1,ta 2 6 A B =...

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1.1. § 1. Vector Spaces 1.1. Introduction 1 . Only the pairs in (b) and (c) are parallel (a) x = (3 , 1 , 2) and y = (6 , 4 , 2) @ 0 6 = t R s.t. y = tx (b) (9 , - 3 , - 21) = 3( - 3 , 1 , 7) (c) (5 , - 6 , 7) = - 1( - 5 , 6 , - 7) (d) x = (2 , 0 , - 5) and y = (5 , 0 , - 2) @ 0 6 = t R s.t. y = tx 2 . (a) x = (3 , - 2 , 4) + t ( - 8 , 9 , - 3) (b) x = (2 , 4 , 0) + t ( - 5 , - 10 , 0) (c) x = (3 , 7 , 2) + t (0 , 0 , - 10) (d) x = ( - 2 , - 1 , 5) + t (5 , 10 , 2) 3 . (a) x = (2 , - 5 , - 1) + s ( - 2 , 9 , 7) + t ( - 5 , 12 , 2) (b) x = ( - 8 , 2 , 0) + s (9 , 1 , 0) + t (14 , - 7 , 0) (c) x = (3 , - 6 , 7) + s ( - 5 , 6 , - 11) + t (2 , - 3 , - 9) (d) x = (1 , 1 , 1) + s (4 , 4 , 4) + t ( - 7 , 3 , 1) 1 PNU-MATH

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1.1. 4 . x = ( a 1 , a 2 , · · · , a n ) R n , i = 1 , 2 , · · · , n 0 = (0 , 0 , · · · , 0) R n s.t. x + 0 = x,
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Unformatted text preview: ) ⇒ tx = t ( a 1 ,a 2 ) = ( ta 1 ,ta 2 ) 6 . A + B = ( a + c,b + d ) , M = ( a + c 2 , b + d 2 ) 7 . C = ( v-u ) + ( w-u ) + u = v + w-u--→ OD + 1 2--→ DB =-→ OA + 1 2-→ AC i.e. w + 1 2 ( v-w ) = 1 2 ( v + w ) = u + 1 2 ( v + w-u-u ) v hO¡S¢P iO£S¤P t d XT] v k h i j t V W X XT^ 2 PNU-MATH...
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