Let S be the subspace of a (2x2) matrix consisting of all symettric (2x2) matrices. Show that S is spanned by the matrices of {(1,0),(0,0)} and {(0,0),(0,1)} ?? How can I do this particular problem?
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A 2x2 symmetric matrix looks like this:
[ a b ]
[ b c ]
take the coefficients a , b and c out:
a{(1,0),(0,0)} +b{(0,1),(1,0)}+c{(0,0),(0,1)}
So S is spanned by
{(1,0),(0,0)},{(0,1),(1,0)} and {(0,0),(0,1)}
you missed one here in your question
[ a b ]
[ b c ]
take the coefficients a , b and c out:
a{(1,0),(0,0)} +b{(0,1),(1,0)}+c{(0,0),(0,1)}
So S is spanned by
{(1,0),(0,0)},{(0,1),(1,0)} and {(0,0),(0,1)}
you missed one here in your question
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Lol !
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