If the system of linear equations x + 2y + 3z = 5 2x + 3y + z = 9 4x + 7y + z = has infinitely many solutions, then the value of + is equal to

Step-by-step solution

For the system of linear equations to have infinitely many solutions, the determinant of the coefficient matrix must be zero. D = vmatrix 1 & 2 & 3 2 & 3 & 1 4 & 7 & vmatrix = 0 Expanding along the first row: 1(3 - 7) - 2(2 - 4) + 3(14 - 12) = 0 3 - 7 - 4 + 8 + 6 = 0 - + 7 = 0 = 7 For the system to be consistent with infinitely many solutions, the same linear dependence that exists among the rows of the coefficient matrix must also hold for the constant terms. Let us find the relation between the rows R₁, R₂, and R