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Joint Entrance Examination
Mathematics
Matrices and Determinants
Question 386
Question 386 of 472
Medium
MCQ
The values of \[\lambda\] and \[\mu\] such that the system of equations
x
+
y
+
z
=
6
x + y + z = 6
x
+
y
+
z
=
6
,
3
x
+
5
y
+
5
z
=
26
3x + 5y + 5z = 26
3
x
+
5
y
+
5
z
=
26
, \[x + 2y + \lambda z = \mu \] has no solution, are :
A
\[\lambda\] = 3, \[\mu\] = 5
B
\[\lambda\] = 3, \[\mu\] \[\ne\] 10
C
\[\lambda\] \[\ne\] 2, \[\mu\] = 10
D
\[\lambda\] = 2, \[\mu\] \[\ne\] 10
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Official solution
x
+
y
+
z
=
6
x + y + z = 6
x
+
y
+
z
=
6
..... (i)
3
x
+
5
y
+
5
z
=
26
3x + 5y + 5z = 26
3
x
+
5
y
+
5
z
=
26
.... (ii) \[x + 2y + \lambda z = \mu \] ..... (iii) \[5 \times (i) - (ii) \Rightarrow 2x = 4 \Rightarrow x = 2\] \[\therefore\] from (i) and (iii)
y
+
z
=
4
y + z = 4
y
+
z
=
4
..... (iv) \[2y + \lambda z = \mu - 2\] .....(v) \[(v) - 2 \times (iv)\] \[ \Rightarrow (\lambda - 2)z = \mu - 10\] \[ \Rightarrow z = {{\mu - 10} \over {\lambda - 2}}\] \& \[y = 4 - {{\mu - 10} \over {\lambda - 2}}\] \[\therefore\] For no solution \[\lambda\] = 2 and \[\mu\] \[\ne\] 10.
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