Originally Posted by

**mazaheri** Consider n linear equations

a11* x1+ a12 * x2 +…+ a1n * xn = b1

a21* x1+ a22 * x2 +…+ a2n * xn = b2

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an1* x1+ an2 * x2 +…+ ann * xn = bn

There are several methods to asses and solve these equations . Finally by any method the solutions x1, x2 ,…, xn are linear combinations of b1, b2 ,…, bn . But

is it possible without any algebraic (or simpler) calculations to show that x1, x2 ,…, xn are such linear combinations?

I am thinking about concepts which predict solutions without a direct effort

to solve. That may be useful in some difficult situations ,of course no this simple example.