A system of linear equations with more equations than unknowns is sometimes called an overdetermined system. Can such a system be consistent? Illustrate your answer with a specific system of three equations in two unknowns.

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Nathalie Redfern · Accepted Answer

The system of linear equation with unknown lesser than the equations. Step 2 Concept: Over-determined system of equations is the system of linear equation with unknowns lesser than the equations. Step 3 The over-determined system is inconsistent with the irregular coefficients. With linear equations they are consistent. To consider a system with three equations but two unknowns, x1+x2=3 2x1−x2=0 3x1+3x2=9 The augmented matrix of the above equations is given below [1132−10339] To apply row application [1132−10339]∼[1130−3−6000] To simplify row 1 and 2 [113012000]∼[101012000] The corresponding system of equation is given below, x1=1 x2=2 The system of equation is consistent and have its unique solution

Jeffrey Jordon · Accepted Answer

Step 1  If we have m equations and n variables where m&amp;gt;n (more equations than variables), then system can be consistent if last m-n equations are linear combinations of previous ones.  For example:  x+y=1  x-y=1  3x+y=3  You can see that third equation is 2×first equation plus 1×second equation.  Solution of system is (x,y)=(1,0)  Result:  If we have m equation and n variables where m&amp;gt;n (more equations than variables), then system can be consistent if last m-n equations are linear combinations of previous ones.

A system of linear equations with more equations than unknowns is sometimes called an overdetermined system. Can such a system be consistent? Illustrate your answer with a specific system of three equations in two unknowns.

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