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  • NOTES 9-7: Augmented Matrices Augmented Matrix:

    Write an augmented matrix that could be used to solve each system of equations.

    Ex. 1: Ex. 2: Ex. 3:

    RULES FOR SOLVING A SYSTEM USING AUGMENTED MATRICES:

    A matrix that is made up of the coefficientsandconstants of a system of equations .

    coefficients I I

    XTZY =35×-451 # *

    ¢÷l¥ coefficients Yonstants

    . Hat :#I get:[My Goal : The coefficientportion of the matrix becomes the identity- matrix . The remaining constants are the solution values .

    * You can always exchange rows

    , or multiplydivide a single row .

    �1� multiply one or two rows so that they become additive inverses .

    �2� Add rows togetherstaff,oy=) to get .

    d- 1

  • Solve these systems of equations using an augmented matrix.

    Ex. 4:

    Ex. 5:

    Ex. 6:

    Note : �1� To get a 1 , divide a row by the number you're changing . �2� Toget a 0 , Make a

    " fake "

    row by multiplying and add rows .

    " fake " row⇐22%retiitiititiikd " ' .oboist;D;¥+.to?iFtiFfoitiThTangeAdd pink T . to 0 row and 2nd solutions !

    row but leave ¥10 , y= -1Original 1st row

    aElitist"÷fii¥.la?t.=toiiiEFtIto:tIt.n * -1 , y=2

    mishit"÷toIM⇒=.to?tD.=toilMx=7 , y

    =3

  • Solve each system of equations using an augmented matrix.

    Ex. 7:

    Ex. 8:

    ;;ftp.t#ItITsEfoili3t.ittitHn=toitIt .

    X = - I , y = -2

    ya⇒ Hy' ' YIIt# " *to :#tank at#a. toHit x= 0 , y = -2