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Unformatted text preview: Set up a double integral which represents the volume under the function and above ! " #$% the triangular region with vertices and . &'( ' ( &*( # ( &'( + (a) (b) (c) 0 0 0 0 0 0 ' $ ' #$ ' ' * $+ * + * $+ #$% .% .$ #$% .% .$ #$% .% .$ (d) ( 0 0 0 0 ' #$ ' #$ * $ * $+ #$% .% .$ #$% .% .$ e) Evaluate ' ' # * $% %/ .%.$ (a) (b) (c) (d) (e) * * * # + # # # # # &/ + &/  # / * /  + &/ * Consider the set of all vectors with , with the usual scalar multiplication and a 12 ( 2 3 2 4 ' * # * new addition: 12 ( 2 3  15 ( 5 3 " 12 5 ( 2  5 3 * # * # * * # # . If this set satisfies Axiom (iv) of a vector space (the existence of a zero vector), what would be the zero vector? (a) (b) (c) (d) (e) 1*( '3 1'( '3 1'( *3 1*( *3 1'( *3 Consider the set of all vectors with , with the usual scalar multiplication and a 12 ( 2 3 2 4 ' * # * new addition: 12 ( 2 3  15 ( 5 3 " 12 5 ( 2  5 3 * # * # * * # # . If this set satisfies Axiom (v) of a vector space (the existence of the negative of a vector), what would be the value of ? 12 ( 2 3 * # (a) (b) (c) (d) (e) 1 ( 2 3 1 2 ( 2 3 12 ( 2 3 1 2 ( 2 3 1 ( 2 3 * * 2 2 * * # * # * # # # * In questions , determine whether the given set is (a) A subspace (b) Closed under addition, but not closed under scalar multiplication (c) Closed under scalar multiplication, but not closed under addition (d) Not closed under addition, and not closed under scalar multiplication The set of vectors where . 12 ( 2 3 2 2 6 ' * # * # The set vectors where . 12 ( 2 3 2  2 " * * # * # The set of all vectors with . 12 ( 2 ( 2 3 2 ( 2 ( 2 7 ' * # # * # + The set of polynomials where . 8&$ " 9  9 $  9 $ 9  9  9 " ' ' * # ' * # # 1....
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This note was uploaded on 04/05/2011 for the course MATH 1zc3 taught by Professor Mclean during the Spring '11 term at McMaster University.
 Spring '11
 McLean
 Math

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