The system of linear equations x+y-z=2, 2x+y-z=3, 3x + 2y + kz = 4 has a unique solution, if k is not equal to

Question

The system of linear equations x+y-z=2, 2x+y-z=3, 3x + 2y + kz = 4 has a unique solution, if k is not equal to (A) 4 (B) -4 (C) 0 (D) 3

Tardigrade Admin · Accepted Answer

The system has a unique solution, if given | beginmatrix1&1&1 2&1&-1 3&2&k endmatrix|≠0 ⇒ 1(k + 2 )-1(2 k + 3) + 1 ( 4 - 3 ) ≠ 0 ⇒ k + 2 - 2k - 3 + 1 ≠ 0 ⇒ k ≠0

Q. The system of linear equations $x + y - z = 2$ , $2 x + y - z = 3$ , $3 x + 2 y + k z = 4$ has a unique solution, if $k$ is not equal to

$4$

$- 4$

$0$

$3$

The system has a unique solution, if
given $∣ ∣ 123112 1 - 1 k ∣ ∣ \neq = 0$
$\Rightarrow 1 (k + 2) - 1 (2 k + 3) + 1 (4 - 3) \neq = 0$
$\Rightarrow k + 2 - 2 k - 3 + 1 \neq = 0 \Rightarrow k \neq = 0$

Q. The system of linear equations x+y−z=2, 2x+y−z=3, 3x+2y+kz=4 has a unique solution, if k is not equal to

4

−4

0

3

The system has a unique solution, if given ∣∣​123​112​1−1k​∣∣​=0 ⇒1(k+2)−1(2k+3)+1(4−3)=0 ⇒k+2−2k−3+1=0⇒k=0

Q. The system of linear equations $x + y - z = 2$ , $2 x + y - z = 3$ , $3 x + 2 y + k z = 4$ has a unique solution, if $k$ is not equal to

$4$

$- 4$

$0$

$3$

The system has a unique solution, if
given $∣ ∣ 123112 1 - 1 k ∣ ∣ \neq = 0$
$\Rightarrow 1 (k + 2) - 1 (2 k + 3) + 1 (4 - 3) \neq = 0$
$\Rightarrow k + 2 - 2 k - 3 + 1 \neq = 0 \Rightarrow k \neq = 0$