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Systems of Linear Equations

Systems of Linear EquationsBeifang Chen1 Systems of Linear equationsLinear systemsAlinear equationin variablesx1, x2, .. , xnis an equation of the forma1x1+a2x2+ +anxn=b,wherea1, a2, .. , anandbare constant real or complex numbers. The constantaiis called thecoefficientofxi; andbis called theconstant termof the of Linear Equations (orlinear system ) is a finite collection of Linear Equations in samevariables. For instance, a Linear system ofmequations innvariablesx1, x2, .. , xncan be written as a11x1+a12x2+ +a1nxn=b1a21x1+a22x2+ +a2nxn= +am2x2+ +amnxn=bm( )Asolutionof a Linear system ( ) is a tuple (s1, s2.)

Systems of linear equations can be represented by matrices. Operations on equations (for eliminating variables) can be represented by appropriate row operations on the corresponding matrices.

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