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If the rank of $[\begin{matrix} x & x & x \\ x & x^{2} & x \\ x & x & x + 1 \end{matrix}]$ is 1, then

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a

x=0(or)x=1

b

x=0

c

x=1

d

x=±2

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detailed solution

Correct option is B

xxxxx2xxxx+1R2−R1,R3−R1~xxx0x2-x0001If rank =1, Thenx2−x=0⇒x(x−1)=0⇒x=0 ∵if x=1, then rank=2Is the possible answer.

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