If the following system of linear equations 2 x + y + z = 5 x - y + z = 3 x + y + a z = b has no solution, then :

Step-by-step solution

Given system of equations 2 x + y + z = 5 x - y + z = 3 x + y + a   z = b has no solution, D = 2 1 1 1 - 1 1 1 1 a = 0 ⇒ - 2 a - 2 - a + 1 + 2 = 0 ⇒ a = 1 3 D 1 = 5 1 1 3 - 1 1 b 1 a = 5 - a - 1   +   - 1 3 a - b   + 1 3 + b   =   - 8 a + 2 b - 2 D 2 = 2 5 1 1 3 1 1 b a = 2 3 a - b   - 5   a - 1 + 1 b - 3   =   a - b + 3 D 3 = 2 1 5 1 - 1 3 1 1 b = 2 - b - 3   -   1   b - 3   +   5 2   =   7 - 3 b For the system to have