MHT CET · Maths · Determinants
For the equations \(x+2 y+3 z=1,2 x+y+3 z=2\) and \(5 x+5 y+9 z=4\)
- A there is only one solution
- B there exists infinitely many solution
- C there is no solution
- D None of the above
Answer & Solution
Correct Answer
(A) there is only one solution
Step-by-step Solution
Detailed explanation
\(\Delta=\left|\begin{array}{ccc}1 & 2 & 3 \\ 2 & 1 & 3 \\ 5 & 5 & 9\end{array}\right|\)
\(=1(9-15)-2(18-15)+3(10-5)\)
\(=-6-6+15=3\neq0\)
Hence, the system of equations has a unique solution.
\(=1(9-15)-2(18-15)+3(10-5)\)
\(=-6-6+15=3\neq0\)
Hence, the system of equations has a unique solution.
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