Matrices - solving two simultaneous equations

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Matrices - solving two simultaneous equationssigma-matrices8-2009-1One of the most important applications of Matrices is to the solution of linear simultaneous this leaflet we explain how this can be simultaneous equations in matrix formConsider the simultaneous equationsx+ 2y= 43x 5y= 1Provided you understand how Matrices are multiplied together you will realise that these can bewritten 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 only unknown is the matrixX,sinceAandBare already called thematrix of the simultaneous equationsGivenAX=Bwe can multiply both sides by the inverse ofA, provided this exists, to giveA 1AX=A 1BButA 1A=I, the identity matrix.

Writing simultaneous equations in matrix form Consider the simultaneous equations x+2y = 4 3x−5y = 1 Provided you understand how matrices are multiplied together you will realise that these can be written in matrix form as 1 2 3 −5! x y! = 4 1! Writing A = 1 2 3 −5!, X = x y!, and B = 4 1! we have AX = B This is the matrix form of the ...

  Equations, Simultaneous, Simultaneous equations