If A is a square matrix of order n such that its elements ar... | MATH - SPECIAL TYPES OF MATRICES, TRANSPOSE, ADJOINT AND INVERSE OF MATRICES | SolveeIt | Solveeit

Today, August 19

Question

If A is a square matrix of order n such that its elements are polynomials in x and its r-rows become identical for x = a, then –

A

(x – a)^r is a factor of |A|

B

(x – a)^{r –1} is a factor of |A|

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C

(x – a)^{r + 1} is a factor of |A|

D

(x – a)^r is a factor of A

Answer

(x – a)^{r –1} is a factor of |A|

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Explanation

Solution

Property, If r rows become identical then

D µ (x – a)^r–1