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Unformatted text preview: A as A + B = [ ab b a ] + [ cd d c ] = [ a + c( b + d ) ( b + d ) a + c ] and the scalar multiplication as α [ ab b a ] = [ αaαb αb αa ] . • Show that the collection ( A ) forms a vector space. • Find a basis of ( A ) and give dim( A ). 2. Inner Product Space (a) Let x = α 1 e 1 + α 2 e 2 and y = β 1 e 1 + β 2 e 2 are a pair of geometric vectors in R 2 . Verify that one may deﬁne the following inner product in R 2 . ( x , y ) = 2 α 1 β 1 + 3 α 2 β 2 . (b) If y 1 , · · · , y n are vectors orthogonal to x , show that any vector in span( y 1 , · · · , y n ) is orthogonal to x ....
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This note was uploaded on 11/22/2010 for the course MATH math 270 taught by Professor Xu during the Winter '07 term at McGill.
 Winter '07
 xu
 Algebra, Vector Space

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