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

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

Postby testing on 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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  TOPIC_SOLVED

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

Sometimes it is that easy! :wink:
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Re: For 2-by-2 matrix A, show that det(sA) = s^2 * det(A)

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

Thanks.
testing
 
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