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Youshouldnowhavethisscreen. Asyoucansee,wehavea3x2matrix

filledwithzeros. Toinputyourownmatrix,typeineachelementofthe

matrixrowbyrow. Thatis,toenterthematrix4 21 38 7,type: ynm

.

Andthisiswhatyoushouldhave. Beforewecanusethismatrix,weneed

tofirstexittheData/MatrixEditor. Todothis,donotpressM!

PressingMwillremovetheselectednumber. Instead,pressthe"

buttontoexittotheHomescreen,ortheObuttontoreturntothe

AppsDesktop.

Toeditthematrix,returntotheData/MatrixEditor,butthistimeselect

Open. ChangethetypetoMatrix,makesureaistheselected

variable,and

press

.

The

matrix

a

will

now

be

displayed

for

editing.

Remembertoalwayspress"orOtoexittheEditor!

Whatifweneedtochangethematrixdimensions? Afteropeningthe

matrix,press2todisplaytheUtilitiesmenuandscrolldownto

ResizeMatrix;press. Typeinthenewdimensionsandpress

toapplythem.

Addingand

Subtracting

Matrices:

Entertwomatricesintothecalculatorasshownabove,oneasaandthe

otherasb. Forthisexample,a=4 21 38 7andb=1 23 45 6. Makesureyou

areattheHomescreenwhileusingmatricesincomputations.

Toaddthesetwomatricestogether,dothefollowing:

j(fora)jc(forb)

Ifdonecorrectly,youshouldseethisscreen.

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Subtractingmatricesissimilar,excepttypeasubtractionsigninsteadofan

additionsign.

(Remember,matricesmustbethesamedimensioninordertoaddor

subtractthem. Thecalculatorwillreturnanerrorifthedimensionsarenot

thesame.)

MultiplyingMatrices:

MatrixmultiplicationiseasyontheTI89. Forscalarmultiplication,multiply

thenumbertimesthematrixjustlikemultiplyingtwonumberstogether.

Forexample,tomultiply3timesthematrixa,type: pj

A.

Multiplyingtwo

matrices

together

is

just

as

easy.

However,

remember

to

havethecorrectmatrixdimensions,otherwisethecalculatorwillgivea

Dimensionerror. Forthisexample,a=4 21 38 7andb=1 2 53 4 5. Try

duplicatingmyscreenbymultiplyingaandbtogether.

Noticethatifthescalarisafraction,theTI89willreturnfractionsinthe

answer. Ifdecimalsaredesired,pressaftertheinitial

multiplication.

UnlikesomeotherTIgraphingcalculatorswithmatrices,theTI89

understandsb/2

to

be

the

same

as

(1/2)b.

CalculatingtheInverse:

Tocalculateamatrixinverse,firstinput5 13 8asmatrixcintotheTI89.(Ofcoursethematrixmustbesquare,otherwisethecalculatorwillreturna

Dimensionerror). Press"toexittotheHomescreen.

PressjCZ.

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GaussianandGaussJordanElimination:

Letsusethesetwomethodstosolvethefollowingsystemofequations:

4 8 2

7 3 142 3 2 3

4 8 1 2

1 7 3 1 42 3 2 3

Inputtheaugmentedmatrixasmatrixa.

Press"toexittheEditor. Letsfirsttrysolvingthesystemusingthe

GaussianEliminationmethod. Press2ztoenterthecalculators

Mathmenu. ScrolldowntoMatrix,presstheBarrowkey,andselectthe

ref(command(RowEchelonForm). Presstopastethe

commandtotheHomescreen.

TypejAdtorunthecommandonmatrixa. Ifa

appears

in

the

answer,

this

means

that

the

matrix

extends

beyond

the

calculatorsscreen;selecttheanswerandusetheAandBarrowkeysto

scrollthematrix.

Notethatifyouswaprows,thematrixgivenbytheref(commandmay

notmatchthematrixobtainedbyperformingtheGaussianeliminationby

hand. Thatisfine;thefinalsolutionwillstillbethesame.

NowletstrytheGaussJordaneliminationmethod. Ifyouhavecalculated

thismethodbyhand,thenyouknowthattheanswerwillbeobtainedat

theend. ThesameappliestotheTI89.

Press2ztoreturntotheMathmenu,butthistimescrolldownto

therref(command(ReducedRowEchelonForm),directlybelowref(.

PresstopastethecommandtotheHomescreen.

TypejAdtorunthecommandonmatrixa.

Therewego! Thesolutiontooursystemofequationsis(3,1,6).

Nowwhatifwehaveadependentorinconsistentsystem? Therref(

commandwillstillworkontheaugmentedmatricesofthesesystems,but

withdifferentresultsthanabove. Foradependentsystem,amatrixwith

thelastrowallzeroswouldbereturned(firstpictureontheright). Foran

inconsistentsystem,amatrixwouldbereturnedwherethelastrow

containsallzerosexceptforafinalelementof1(secondpictureonthe

right).

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Determinants:

Inputthismatrixasmatrixainthecalculator:4 2 15 7 21 3 5Tocalculatethedeterminantofa,press2ztoenterthe

calculatorsMath

menu,

scroll

down

to

Matrix,

press

the

B

arrow

key

and

selectthedet(command. Presstopastethecommandtothe

Homescreen. TypejAdtorunthecommandon

matrixa. Thatsit! Thedeterminantofthismatrixis96.

Transpose:

Letscalculate

the

transpose

of

4 2 15 7 21 3 5. Ifitisnottherealready,inputthismatrixasainthecalculator. Pressjtotypeaonthe

Homescreen,thengobacktotheMathmenu,entertheMatrixsubmenu

andselectthefirstcommand. Presstopastethecommandtothe

screen,andthenagaintorunthecommand.

DeletingMatricesfromtheCalculator:

DeletingmatricesfromtheTI89isnottoohard,butwemustbecareful.

Wewillbeenteringanareaofthecalculatorwherewecouldpossibly

deletesomethingthatwedidnotintendto. First,press2

(abovethe|key). UsetheCandDarrowkeystoselectthematrixyou

wanttodelete,andthenpressthe0key. PresstoconfirmorN

tocancel. Makesuretopress"toreturntotheHomescreen.