Question 19 - 2021 (24 Feb Shift 2)

For the system of linear equations: $x - 2y = 1$, $x - y + kz = -2$, $ky + 4z = 6$, $k \in \mathbb{R}$

consider the following statements:

(A) The system has unique solution if $k \neq 2, k \neq -2$. (B) The system has unique solution if $k = -2$. (C) The system has unique solution if $k = 2$. (D) The system has no-solution if $k = 2$. (E) The system has infinite number of solutions if $k \neq -2$.

Which of the following statements are correct?

(1) $(B)$ and $(E)$ only

(2) $(C)$ and $(D)$ only

(3) $(A)$ and $(D)$ only

(4) $(A)$ and $(E)$ only