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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 .
Solve these systems of equations using an augmented matrix.
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
Solve each system of equations using an augmented matrix.
X = - I , y = -2
ya⇒ Hy' ' YIIt# " *to :#tank at#a. toHit x= 0 , y = -2