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Joint Entrance Examination
Mathematics
Matrices and Determinants
Question 46
Question 46 of 472
Medium
MCQ
The system of equations
x
+
y
+
z
=
6
,
x
+
2
y
+
5
z
=
9
,
x
+
5
y
+
λ
z
=
μ
,
\begin{gathered} x+y+z=6, \\ x+2y+5z=9, \\ x+5y+\lambda z=\mu , \end{gathered}
x
+
y
+
z
=
6
,
x
+
2
y
+
5
z
=
9
,
x
+
5
y
+
λ
z
=
μ
,
has no solution if
A
λ
=
17
,
μ
=
18
\lambda =17,\mu =18
λ
=
17
,
μ
=
18
B
λ
=
17
,
μ
≠
18
\lambda =17,\mu \ne 18
λ
=
17
,
μ
=
18
C
λ
=
15
,
μ
≠
17
\lambda =15,\mu \ne 17
λ
=
15
,
μ
=
17
D
λ
≠
17
,
μ
≠
18
\lambda \ne 17,\mu \ne 18
λ
=
17
,
μ
=
18
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Official solution
D
=
∣
1
1
1
1
2
5
1
5
λ
∣
=
0
λ
=
17
D
z
=
∣
1
1
6
1
2
9
1
5
μ
∣
≠
0
μ
≠
18
\begin{gathered} D=|\begin{array}{|c|}1 \quad 1 \quad 1 \\ 1 \quad 2 \quad 5 \\ 1 \quad 5 \quad \lambda\end{array}|=0 \\ \lambda =17 \\ {D}_{z}=|\begin{array}{|c|}1 \quad 1 \quad 6 \\ 1 \quad 2 \quad 9 \\ 1 \quad 5 \quad \mu\end{array}|\ne 0 \\ \mu \ne 18 \end{gathered}
D
=
∣
1
1
1
1
2
5
1
5
λ
∣
=
0
λ
=
17
D
z
=
∣
1
1
6
1
2
9
1
5
μ
∣
=
0
μ
=
18
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