The number of θ ∈(0,4 π) for which the system of linear equations 3( sin 3 θ) x-y+z=2 3( cos 2 θ) x+4 y+3 z=3 6 x+7 y+7 z=9 has no solution is :

Question

The number of θ ∈(0,4 π) for which the system of linear equations 3( sin 3 θ) x-y+z=2 3( cos 2 θ) x+4 y+3 z=3 6 x+7 y+7 z=9 has no solution is : (A) 6 (B) 7 (C) 8 (D) 9

Tardigrade Admin · Accepted Answer

The system of equation has no solution. D = |3 sin 3 θ -1 1 3 cos 2 θ 4 3 6 7 7|=0 21 sin 3 θ+42 cos 2 θ-42=0 sin 3 θ+2 cos 2 θ-2=0 Number of solution is 7 in (0,4 π)

Q. The number of $θ \in (0, 4 π)$ for which the system of linear equations
$3 (sin 3 θ) x - y + z = 2$
$3 (cos 2 θ) x + 4 y + 3 z = 3$
$6 x + 7 y + 7 z = 9$
has no solution is :

6

7

8

9

The system of equation has no solution.
$D = ∣ ∣ 3 sin 3 θ 3 cos 2 θ 6 - 1 47 137 ∣ ∣ = 0$
$21 sin 3 θ + 42 cos 2 θ - 42 = 0$
$sin 3 θ + 2 cos 2 θ - 2 = 0$
Number of solution is 7 in $(0, 4 π)$

Q. The number of θ∈(0,4π) for which the system of linear equations 3(sin3θ)x−y+z=2 3(cos2θ)x+4y+3z=3 6x+7y+7z=9 has no solution is :

6

7

8

9

The system of equation has no solution. D=∣∣​3sin3θ3cos2θ6​−147​137​∣∣​=0 21sin3θ+42cos2θ−42=0 sin3θ+2cos2θ−2=0 Number of solution is 7 in (0,4π)

Q. The number of $θ \in (0, 4 π)$ for which the system of linear equations
$3 (sin 3 θ) x - y + z = 2$
$3 (cos 2 θ) x + 4 y + 3 z = 3$
$6 x + 7 y + 7 z = 9$
has no solution is :

The system of equation has no solution.
$D = ∣ ∣ 3 sin 3 θ 3 cos 2 θ 6 - 1 47 137 ∣ ∣ = 0$
$21 sin 3 θ + 42 cos 2 θ - 42 = 0$
$sin 3 θ + 2 cos 2 θ - 2 = 0$
Number of solution is 7 in $(0, 4 π)$