Let P ( x ) be the determinant with Row 1: a 1 , x , x ; Row 2: x , a 2 , x ; Row 3: x , x , a 3 . If P ( x ) = xg ( x ) − f ( x ) and f ( x ) = ( x − a 1 ) ( x − a 2 ) ( x − a 3 ) , find

Question

Let P ( x ) be the determinant with Row 1: a 1 ​ , x , x ; Row 2: x , a 2 ​ , x ; Row 3: x , x , a 3 ​ . If P ( x ) = xg ( x ) − f ( x ) and f ( x ) = ( x − a 1 ​ ) ( x − a 2 ​ ) ( x − a 3 ​ ) , find g ( x ) .

TestHub · Accepted Answer

Column and row operations give P ( x ) = x ′ ( x ) − f ( x ) , hence g ( x ) = f ′ ( x ) , which is option C.

Mathematics - Matrices Question with Solution | TestHub

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