99 Percentile Qs Bank for JEE MainMathematicsMatrices
The rank of A= [ array ccc 1 & x & x+1 2 x & x^2-x & x^2+x 3 x(x-1) & x (x^2-3 x+2 ) & x (x^2-1 ) array ] is
Options
- A3 ; for all x R
- B2 ; only for x=-1
- C2 ; for all x except 0,1 and -1
- D3 ; only for x=0
Correct answer
C. 2 ; for all x except 0,1 and -1
Step-by-step solution
We have, A= | array ccc 1 & x & x+1 2 x & x^2-x & x^2+x 3 x(x-1) & x (x^2-3 x+2 ) & x (x^2-1 ) array | aligned & A=x^2(x-1) | array ccc 1 & x & x+1 2 & x-1 & x+1 3 & x-2 & x+1 array | & A=x(x-1) | array ccc 1 & x & x+1 0 & x-1-2 x & x+1-2 x-2 0 & x-2-3 x & x+1-3 x-3 array | & A=x(x-1) | array ccc 1 & x & x+1 0 & x^2-3 x & x^2-x-2 0 & -2 x-2 & -2 x-2 array | aligned gathered A=x(x-1)(-2 x-2) | array ccc 1 & x & x+1 0 & x^2-3 x & x^2-x-2 0 & 1 & 1 array | A=-2 x(x-1)(x+1) (x^2-3 x-x^2+x+2 ) A=-2 x(x-1)(x+1)(-2 x+2) A