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December 12th, 2014, 06:19 PM   #1
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Relationship between singular matrices and linear dependency?

I know that when a matrix is singular it has no inverse and its determinant is 0.
How does that relate to its linear dependency?
How can I tell or prove this to myself?
and is it the columns or rows that are linearly dependent?

Last edited by skipjack; December 12th, 2014 at 08:07 PM.
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December 12th, 2014, 08:20 PM   #2
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For a simple example, consider

a b
c d

(where a is non-zero).

If the determinant is zero, ad = bc, so the second row is c/a times the first row and the second column is b/a times the first column.
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