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Question

Using Cofactors of elements of second row, evaluate .

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Solution

Given determinant is,

| 5 3 8 2 0 1 1 2 3 |

Minor of a 21 is,

M 21 =| 3 8 2 3 | =916 =7

Minor of a 22 is,

M 22 =| 5 8 1 3 | =158 =7

Minor of a 23 is,

M 23 =| 5 3 1 2 | =103 =7

Cofactor of a 21 is,

A 21 = ( 1 ) 2+1 ( 7 ) =7

Cofactor of a 22 is,

A 22 = ( 1 ) 2+2 ( 7 ) =7

Cofactor of a 23 is,

A 23 = ( 1 ) 2+3 ( 7 ) =7

The value of the given determinant is,

Δ= a 21 A 21 + a 22 A 22 +a23 A 23 =2×7+0×7+1×( 7 ) =147 =7


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