NOTES 9-7: Augmented Matrices€¦ · NOTES 9-7: Augmented Matrices Augmented Matrix: # Write an...

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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 coefficients and constants of a system of equations coefficients I I XTZY =3 5×-451 # * ¢÷l¥ coefficients Yonstants . Hat :# I get :[ My Goal : The coefficient portion of the matrix becomes the identity - matrix The remaining constants are the solution values * You can always exchange rows , or multiply divide a single row !1! multiply one or two rows so that they become additive inverses !2! Add rows together staff ,oy= ) to get d- 1

Transcript of NOTES 9-7: Augmented Matrices€¦ · NOTES 9-7: Augmented Matrices Augmented Matrix: # Write an...

Page 1: NOTES 9-7: Augmented Matrices€¦ · NOTES 9-7: Augmented Matrices Augmented Matrix: # Write an augmented matrix that could be used to solve each system of equations. Ex. 1: Ex.

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

Page 2: NOTES 9-7: Augmented Matrices€¦ · NOTES 9-7: Augmented Matrices Augmented Matrix: # Write an augmented matrix that could be used to solve each system of equations. Ex. 1: Ex.

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

Page 3: NOTES 9-7: Augmented Matrices€¦ · NOTES 9-7: Augmented Matrices Augmented Matrix: # Write an augmented matrix that could be used to solve each system of equations. Ex. 1: Ex.

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