What can be said about the solution of the system of equations:
= 0, + = 0, + + = 0
(a) No solution
(b) A unique trivial solution
(c) Three solutions
(d) Infinite solutions .
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Answer:
(b)A unique trivial solution
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An n×n homogeneous system of linear equations has a unique solution (the trivial solution) if and only if its determinant is non-zero. If this determinant is zero, then the system has an infinite number of solutions. i.e. For a non-trivial solution ∣A∣=0.
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