Project ForgeEngineering Mathematics
Linear Algebra
GATE 2011
Medium
Consider the following system of equations: 2x1+x2+x3=0, x2-x3=0, x1+x2=0. This system has
- Aa unique solution
- Bno solution
- infinite number of solutions
- Dfive solutions
Explanation
This is a homogeneous system (all RHS = 0), so it always has at least the trivial solution. The coefficient matrix [[2,1,1],[0,1,-1],[1,1,0]] has determinant 2(0+1)-1(0+1)+1(0-1)=2-1-1=0, so the rows are linearly dependent and the system has infinitely many (non-trivial) solutions.
Source: GATE ME 2011 (2011)
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