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Joint Entrance Examination
Mathematics
Matrices and Determinants
Question 385
Question 385 of 472
Medium
MCQ
The value of k \[\in\]R, for which the following system of linear equations 3x - y + 4z = 3, x + 2y - 3z = -2 6x + 5y + kz = -3, has infinitely many solutions, is :
A
3
B
\[-\]5
C
5
D
\[-\]3
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Official solution
\[\left| {
(
3
−
1
4
1
2
−
3
6
5
k
)
\begin{pmatrix} 3 & { - 1} & 4 \\ 1 & 2 & { - 3} \\ 6 & 5 & k \\ \end{pmatrix}
3
1
6
−
1
2
5
4
−
3
k
} \right| = 0\] \[\Rightarrow\] 3(2k + 15) + K + 18 - 28 = 0 \[\Rightarrow\] 7k + 35 = 0 \[\Rightarrow\] k = - 5
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