The rank of the matrix 4 2 ( 1 - x ) 5 k 1 6 3 ( 1 + x ) is 1 , then

Step-by-step solution

Given that Rank of the matrix 4 2 ( 1 - x ) 5 k 1 6 3 ( 1 + x ) is 1 . We know that, Rank of Matrix is number of non-zero rows of a matrix in its echelon form. Applying R 3 → R 1 + R 3 ⇒ 4 2 ( 1 - x ) 5 k 1 10 5 2 Now, Applying R 3 → R 3 - 2 R 2 ⇒ 4 2 ( 1 - x ) 5 k 1 0 5 - 2 k 0 Now, Applying R 2 → R 2 - 5 4 R 1 ⇒ 4 2 ( 1 - x ) 0 k - 5 2 5 x - 1 4 0 5 - 2 k 0 Rank of Matrix is 1 ⇒ k - 5 2 = 0 ,   5 x - 1 4 = 0 ,   5 - 2 k = 0 ∴ k = 5 2 ,   x = 1 5