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Joint Entrance Examination
Mathematics
Matrices and Determinants
Question 24
Question 24 of 472
Medium
MCQ
If the system of equations
3
x
+
y
+
4
z
=
3
3x+y+4z=3
3
x
+
y
+
4
z
=
3
2
x
+
α
y
−
z
=
−
3
2x+\alpha y-z=-3
2
x
+
α
y
−
z
=
−
3
x
+
2
y
+
z
=
4
x+2y+z=4
x
+
2
y
+
z
=
4
has no solution, then the value of
α
\alpha
α
is equal to:
A
13
B
4
C
19
D
23
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Official solution
Δ
=
∣
3
1
4
2
α
−
1
1
2
1
∣
det
(
Δ
)
=
0
α
=
19
\begin{gathered} \Delta=|\begin{array}{|c|}3 \quad 1 \quad 4 \\ 2 \quad \alpha \quad -1 \\ 1 \quad 2 \quad 1\end{array}| \\ \det (\Delta)=0 \\ \alpha =19 \end{gathered}
Δ
=
∣
3
1
4
2
α
−
1
1
2
1
∣
det
(
Δ
)
=
0
α
=
19
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