Consider the system of linear equations x sin α-3 y cos α- kz =0 ; 2 x + y + z =0,- x + y + 2 z =0 then

Question

Consider the system of linear equations x sin α-3 y cos α- kz =0 ; 2 x + y + z =0,- x + y + 2 z =0 then (A) the number of integral values of k for which system of equations has non-trivial solution are 11. (B) for k=-4 the system of equation has infinite solution. (C) for k=6 the system of equation has unique solution. (D) for k=-6 the system of equation has trivial solution.

Tardigrade Admin · Accepted Answer

| sin α -3 cos α - k 2 1 1 -1 1 2|=0 sin α+3 cos α(5)- k (3)=0 sin α+15 cos α=3 k -√226 ≤ 3 k ≤ √226 -(√226/3) ≤ k ≤ (√226/3) So, 11 integral values of ' k '.

Q. Consider the system of linear equations $x sin α - 3 y cos α - k z = 0; 2 x + y + z = 0, - x + y +$ $2 z = 0$ then

the number of integral values of $k$ for which system of equations has non-trivial solution are 11.

for $k = - 4$ the system of equation has infinite solution.

for $k = 6$ the system of equation has unique solution.

for $k = - 6$ the system of equation has trivial solution.

$∣ ∣ sin α 2 - 1 - 3 cos α 11 - k 12 ∣ ∣ = 0$
$sin α + 3 cos α (5) - k (3) = 0$
$sin α + 15 cos α = 3 k$
$- 226 \leq 3 k \leq 226$
$- \frac{226}{3} \leq k \leq \frac{226}{3}$
So, 11 integral values of ' $k$ '.

Q. Consider the system of linear equations xsinα−3ycosα−kz=0;2x+y+z=0,−x+y+ 2z=0 then

the number of integral values of k for which system of equations has non-trivial solution are 11.

for k=−4 the system of equation has infinite solution.

for k=6 the system of equation has unique solution.

for k=−6 the system of equation has trivial solution.