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Joint Entrance Examination
Mathematics
Matrices and Determinants
Question 391
Question 391 of 472
Medium
MCQ
The values of a and b, for which the system of equations 2x + 3y + 6z = 8 x + 2y + az = 5 3x + 5y + 9z = b has no solution, are :
A
a = 3, b \[\ne\] 13
B
a \[\ne\] 3, b \[\ne\] 13
C
a \[\ne\] 3, b = 3
D
a = 3, b = 13
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Official solution
\[D = \left| {
(
2
3
6
1
2
a
3
5
9
)
\begin{pmatrix} 2 & 3 & 6 \\ 1 & 2 & a \\ 3 & 5 & 9 \\ \end{pmatrix}
2
1
3
3
2
5
6
a
9
} \right| = 3 - a\] \[D = \left| {
(
2
3
8
1
2
5
3
5
b
)
\begin{pmatrix} 2 & 3 & 8 \\ 1 & 2 & 5 \\ 3 & 5 & b \\ \end{pmatrix}
2
1
3
3
2
5
8
5
b
} \right| = b - 13\] If a = 3, b \[\ne\] 13, no solution.
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