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Evaluation of a Determinant

If, find .

Question

If , find .

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Solution

The given matrix is,

A=[ 1 1 −2 2 1 −3 5 4 −9 ]

Determinant of the given matrix is,

| A |=| 1 1 −2 2 1 −3 5 4 −9 | =1| 1 −3 4 −9 |−1| 2 −3 5 −9 |+( −2 )| 2 1 5 4 | =3( 1×( −9 )−( −3 )×4 )−1( 2×( −9 )−5×( −3 ) )−2( 2×( 4 )−1×5 ) =0

Thus, the value of determinant is 0.

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