The simultaneous equations k x+2 y-z=1 (k-1) y-2 z=2 (k+2) z=3 have only one solution when

Question

The simultaneous equations k x+2 y-z=1 (k-1) y-2 z=2 (k+2) z=3 have only one solution when (A) k=-2 (B) k=-1 (C) k=0 (D) k=1

Tardigrade Admin · Accepted Answer

The system of given equations is k x+2 y-z=1 (k-1) y-2 z=2 and (k+2) z=3 This system of equations has unique solution, if | k 2 -1 0 k-1 -2 0 0 k+2| ≠ 0 ⇒ (k+2)(k)(k-1) ≠ 0 ⇒ k ≠-2,0,1 i.e., k=-1, is a required answer.

Q. The simultaneous equations
$k x + 2 y - z = 1$
$(k - 1) y - 2 z = 2$
$(k + 2) z = 3$
have only one solution when

$k = - 2$

$k = - 1$

$k = 0$

$k = 1$

Q. The simultaneous equations kx+2y−z=1 (k−1)y−2z=2 (k+2)z=3 have only one solution when

k=−2

k=−1

k=0

k=1

The system of given equations is kx+2y−z=1 (k−1)y−2z=2 and (k+2)z=3 This system of equations has unique solution, if ∣∣​k00​2k−10​−1−2k+2​∣∣​=0 ⇒(k+2)(k)(k−1)=0 ⇒k=−2,0,1 i.e., k=−1, is a required answer.

Q. The simultaneous equations
$k x + 2 y - z = 1$
$(k - 1) y - 2 z = 2$
$(k + 2) z = 3$
have only one solution when

$k = - 2$

$k = - 1$

$k = 0$

$k = 1$