questionr
Early access
Exams
Joint Entrance Examination
Mathematics
Matrices and Determinants
Question 366
Question 366 of 472
Medium
MCQ
If the system of equations x+y+z=2 2x+4y--z=6 3x+2y+\[\lambda \]z=\[\mu \] has infinitely many solutions, then
A
2\[\lambda \] - \[\mu \] = 5
B
\[\lambda \] - 2\[\mu \] = -5
C
2\[\lambda \] + \[\mu \] = 14
D
\[\lambda \] + 2\[\mu \] = 14
Check answer
Press A-D to select · Enter to check
Solutions · 1
Post your solution
Official solution
\[D = 0\,\left| {
(
1
1
1
2
4
−
1
3
2
λ
)
\begin{pmatrix} 1 & 1 & 1 \\ 2 & 4 & { - 1} \\ 3 & 2 & \lambda \\ \end{pmatrix}
1
2
3
1
4
2
1
−
1
λ
} \right| = 0\] \[ \Rightarrow \] \[(4\lambda + 2) - 1(2\lambda + 3) + 1(4 - 12) = 0\] \[ \Rightarrow \] \[4\lambda + 2\] \[ - 2\lambda - 3\]
−
-
−
8
=
0
= 0
=
0
⇒
\Rightarrow
⇒
2
λ
=
9
⇒
λ
=
9
2
2\lambda = 9 \Rightarrow \lambda = {9 \over 2}
2
λ
=
9
⇒
λ
=
2
9
D
x
=
∣
(
2
1
1
6
4
−
1
μ
2
−
9
/
2
)
∣
=
0
{D_x} = \left| {\begin{pmatrix} 2 & 1 & 1 \\ 6 & 4 & { - 1} \\ \mu & 2 & { - 9/2} \\ \end{pmatrix} } \right| = 0
D
x
=
2
6
μ
1
4
2
1
−
1
−
9/2
=
0
\Rightarrow \mu = 5\[ By checking all the options we find (C) is correct \]2\lambda + \mu = 14
Answer the question to unlock
Previous
Next