If the matrix A= [ array ccc y+a & b & c a & y+b & c a & b & y+c array ] has rank 3, then

Step-by-step solution

Here, the rank of A is 3 . Therefore, the minor of order 3 of A 0 | array ccc y+a & b & c a & y+b & c a & b & y+c array | 0 [Applying C₁ C₁+C₂+C₃ and taking (y+a+b+c) common from .C₁ ] (y+a+b+c) | array ccc 1 & b & c 1 & y+b & c 1 & b & y+c array | 0 [Applying R₂ R₂-R₁, R₃ R₃-R₁ ] (y+a+b+c) | array lll 1 & b & c 0 & y & 0 0 & 0 & y array | 0 Expanding along C₁ (y+a+b+c) (y^2 ) 0 y 0 and y -(a+b+c)