JEE MAIN - Mathematics (2021 - 25th July Morning Shift - No. 11)
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 :
2x + 3y + 6z = 8
x + 2y + az = 5
3x + 5y + 9z = b
has no solution, are :
a = 3, b $$\ne$$ 13
a $$\ne$$ 3, b $$\ne$$ 13
a $$\ne$$ 3, b = 3
a = 3, b = 13
Explanation
$$D = \left| {\matrix{
2 & 3 & 6 \cr
1 & 2 & a \cr
3 & 5 & 9 \cr
} } \right| = 3 - a$$
$$D = \left| {\matrix{ 2 & 3 & 8 \cr 1 & 2 & 5 \cr 3 & 5 & b \cr } } \right| = b - 13$$
If a = 3, b $$\ne$$ 13, no solution.
$$D = \left| {\matrix{ 2 & 3 & 8 \cr 1 & 2 & 5 \cr 3 & 5 & b \cr } } \right| = b - 13$$
If a = 3, b $$\ne$$ 13, no solution.
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