The value of k ∈ R , for which the following system of linear equations 3 x - y + 4 z = 3 x + 2 y - 3 z = - 2 6 x + 5 y + k z = - 3 has infinitely many solutions, is:

Step-by-step solution

We have, 3 x - y + 4 z = 3 x + 2 y - 3 z = - 2 6 x + 5 y + k z = - 3 For infinitely many solutions, A = 0 ⇒ 3 - 1 4 1 2 - 3 6 5   k = 0 ⇒ 3 ( 2 k + 15 ) + 1 k + 18 + 4 5 - 12 = 0 ⇒ 3 ( 2 k + 15 ) + k + 18 - 28 = 0 ⇒ 7 k + 35 = 0 ⇒ k = - 5