For 2-by-2 matrix A, show that det(sA) = s^2 * det(A)

Linear spaces and subspaces, linear transformations, bases, etc.
testing
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For 2-by-2 matrix A, show that det(sA) = s^2 * det(A)

Postby testing » Sun Mar 01, 2009 7:15 pm

Let A be any 2-by-2 matrix, and let s be any real-valued scalar. Show that det (sA) = s2 * det (A).

A = [ a  b ]  sA = [ sa sb ]
[ c d ] [ sc sd ]

det(A) = ad - cb

det(sA) = (sa)(sd) - (sc)(sb)

= s^2(ad) - s^2(cb)

= s^2 * det(A)

This seems too easy?

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stapel_eliz
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Postby stapel_eliz » Sun Mar 01, 2009 7:35 pm

Sometimes it is that easy! :wink:

testing
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Re: For 2-by-2 matrix A, show that det(sA) = s^2 * det(A)

Postby testing » Wed Mar 04, 2009 7:35 pm

Thanks.


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