Question

The given set of equations has at least one non trivial solution.

x + 3y + 2z =0

2x + y + 4z = 0

x + 11y + 14z =0

• A. True
• B. False

Answer 1

The correct option is A

True

$Here,AX=B\left[\begin{array}{ccc}1& 3& -2\\ 2& -1& 4\\ 1& -11& 14\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{c}0\\ 0\\ 0\end{array}\right]\text{Given is a Homogeneous set of equations this will have non trivial solutions only if}\left|A\right|=0.Here,\left|A\right|=1(-14+44)-3(28-4)-2(-22+1)=30-72+42=0.\therefore \text{It has infinite solutions Implies it has non trivial solutions too.}$