5.6 Using the inverse matrix to solve equations

The inverse matrix tosolve equationsIntroductionOne of the most important applications of matrices is to the solution of linear simultaneousequations. On this leaflet we explain how this can be Writing simultaneous equations in matrix formConsider the simultaneous equationsx+ 2y= 43x 5y= 1 Provided you understand how matrices are multiplied together you will realise that these canbe written in matrix form as(1 23 5)(xy)=(41)WritingA=(1 23 5),X=(xy),andB=(41)we haveAX=BThis is thematrix formof the simultaneous equations . Here the unknown is the matrixX,sinceAandBare already called thematrix of Solving the simultaneous equationsGivenAX=Bwe can multiply both sides by the inverse ofA, provided this exists, to giveA 1AX=A 1 BButA 1A=I, the identity matrix .

Using the inverse matrix to solve equations Introduction One of the most important applications of matrices is to the solution of linear simultaneous equations. On this leaflet we explain how this can be done. 1. Writing simultaneous equations in matrix form

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