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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