Unformatted text preview: ) 8. Set U = { ( a b c )  abc = 6; a,b,c ∈ R } , a subset of R 3 . Give three vectors from U , and determine whether or not U is a vector space. (10 Points ) 9. Determine if the set of all 3 × 3 diagonal matrices is a vector space under the usual matrix addition and scalar multiplication. (10 Points ) BONUS. Let F [ a,b ] be the set of all real valued functions that are deﬁned on the interval [ a,b ]. Then given any two “vectors”, f = f ( x ) and g = g ( x ), from F [ a,b ] and any scalar c , deﬁne addition and scalar multiplication as, ( f + g )( x ) = f ( x ) + g ( x ) and c f = cf ( x ), respectively. Under these operations F [ a,b ] is a vector space. Find the “zero vector” for F [ a,b ]. (3 Points )...
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 Spring '16
 Prof. Ruivivar
 Linear Algebra, Vector Space

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