Let , R be such that the system of linear equations x + 2y + z = 5 2x + y + z = 5 8x + 4y + z = 18 has no solution. Then is equal to :

Step-by-step solution

The given system of linear equations is: x + 2y + z = 5 2x + y + z = 5 8x + 4y + z = 18 For the system to have no solution, the determinant of the coefficient matrix D must be zero. D = vmatrix 1 & 2 & 1 2 & 1 & 8 & 4 & vmatrix = 0 Expanding along the first row: 1( - 4 ) - 2(2 - 8 ) + 1(8 - 8) = 0 - 4 - 4 + 16 = 0 12 - 3 = 0 = 4 To verify the no solution condition, substitute = 4 into the third equation: 8x + 4y + 4 z = 18 4(2x + y + z) = 18 2x + y + z = 9 2 However, the second equation is 2x + y + z = 5 . This res