Example 3: A space spanned by a set of vectors
The vector space L ( 1, 2, ... , n ) spanned by the vectors { 1, 2, ... , n },

1 = { 1, 0, 0, ... , 0 },
2 = { 0, 1, 0, ... , 0 },
:
n = { 0, 0, 0, ... , 1 }.

is Rn, since for every = ( x1, x2, ... , xn ) Rn :
= x11 + x22 + ... + xnn
( = ( x1, 0, ... , 0 ) + ( 0, x2, ... , 0 ) + ... + ( 0, 0, ... , xn ) )

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