A value of b for which the rank of the matrix A= [ array cccc 1 & 1 & -1 & 0 4 & 4 & -3 & 1 b & 2 & 2 & 2 9 & 9 & b & 3 array ] is 3 , is

Step-by-step solution

Given, A= [ array cccc 1 & 1 & -1 & 0 4 & 4 & -3 & 1 b & 2 & 2 & 2 9 & 9 & b & 3 array ] For rank to be 3, there must exist 3 non zero row. Now, applying R₂ R₂-4 R₁ ; R₃ R₃-2 R₁ = [ array cccc 1 & 1 & -1 & 0 0 & 0 & 1 & 1 b-2 & 0 & 4 & 2 9 & 9 & b & 3 array ] Applying R₄ R₄-9 R₁ = [ array cccc 1 & 1 & -1 & 0 0 & 0 & 1 & 1 b-2 & 0 & 4 & 2 0 & 0 & b+9 & 3 array ] Again, applying R₄ R₄-3 R₂ A= [ array cccc 1 & 1 & -1 & 0 0 & 0 & 1 & 1 b-2 & 0 & 4 & 2 0 & 0 & b+6 & 0 array ] If rank =3 , then Last row must have all ele