Question

Which of the following options holds true for the system of equations,

x + y + z =6

x + 2y + 3z = 12

x + 4y + 7z =30

• A. No solution
• B. Infinite solution
• C. Trivial solution only
• D. Unique Non trivial solutions

Answer 1

The correct option is A

No solution

$AX=B\left[\begin{array}{ccc}1& 1& 1\\ 1& 2& 3\\ 1& 4& 7\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{c}6\\ 12\\ 30\end{array}\right]Adj.B=\left[\begin{array}{ccc}2& -3& 1\\ -4& 6& -2\\ 2& -3& 1\end{array}\right].\left[\begin{array}{c}6\\ 12\\ 30\end{array}\right]=\left[\begin{array}{c}6\\ -12\\ 6\end{array}\right]\ne 0.\text{We know when}\left|A\right|0andadjA.B\ne 0\text{then there exists no solution of the given system of equations.}$