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Joint Entrance Examination
Mathematics
Matrices and Determinants
Question 104
Question 104 of 472
Medium
MCQ
The following system of linear equations 7x + 6y -- 2z = 0 3x + 4y + 2z = 0 x -- 2y -- 6z = 0, has
A
no solution
B
infinitely many solutions, (x, y, z) satisfying y = 2z
C
infinitely many solutions, (x, y, z) satisfying x = 2z
D
only the trivial solution
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Official solution
Given 7x + 6y -- 2z = 0 .......(1) 3x + 4y + 2z = 0 ......(2) x -- 2y -- 6z = 0 .......(3) \[\Delta \] = \[\left| {
(
7
6
−
2
3
4
2
1
−
2
−
6
)
\begin{pmatrix} 7 & 6 & { - 2} \\ 3 & 4 & 2 \\ 1 & { - 2} & { - 6} \\ \end{pmatrix}
7
3
1
6
4
−
2
−
2
2
−
6
} \right|\] = 7(--24 + 4) -- 6(--18 -- 2) -- 2(--6 -- 4) = 0 \[ \therefore \] \[\Delta \] = 0 The system of equation has infinite non-trival solution. Also adding equation (1) and 3\[ \times (3), we get 10x = 20z \[ \Rightarrow \] x = 2z
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