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:[MyGoal : 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= -1
Original 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. toHitx= 0
, y = -2