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Matrices

AMatrixisanarrayofnumbers:

AMatrix

(Thisonehas2Rowsand3Columns)

Wetalkaboutonematrix,orseveralmatrices.

Therearemanythingswecandowiththem...

AddingToaddtwomatrices:addthenumbersinthematchingpositions:

Thesearethecalculations:

3+4=7 8+0=8

4+1=5 69=3

Thetwomatricesmustbethesamesize,i.e.therowsmustmatchinsize,andthecolumnsmustmatchinsize.

Example:amatrixwith3rowsand5columnscanbeaddedtoanothermatrix

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of3rowsand5columns.

Butitcouldnotbeaddedtoamatrixwith3rowsand4columns(thecolumnsdon'tmatchinsize)

NegativeThenegativeofamatrixisalsosimple:

Thesearethecalculations:

(2)=2 (4)=+4

(7)=7 (10)=10

SubtractingTosubtracttwomatrices:subtractthenumbersinthematchingpositions:

Thesearethecalculations:

34=1 80=8

41=3 6(9)=15

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Note:subtractingisactuallydefinedastheadditionofanegativematrix:A+(B)

Multiply by a ConstantWecanmultiplyamatrixbysomevalue:

Thesearethecalculations:

24=8 20=0

21=2 29=18

Wecalltheconstantascalar,soofficiallythisiscalled"scalarmultiplication".

Multiplying by Another MatrixTomultiplytwomatricestogetherisabitmoredifficult...read MultiplyingMatrices tolearnhow.

DividingAndwhataboutdivision?Wellwedon'tactuallydividematrices,wedoitthisway:

A/B=A(1/B)=AB1

whereB1meansthe"inverse"ofB.

Sowedon'tdivide,insteadwemultiplybyaninverse.

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AndtherearespecialwaystofindtheInverse...

...learnmoreaboutthe InverseofaMatrix .

TransposingTo"transpose"amatrix,swaptherowsandcolumns.Weputa"T"inthetoprighthandcornertomeantranspose:

NotationAmatrixisusuallyshownbyacapitalletter(suchasA,orB)

Eachentry(or"element")isshownbyalowercaseletterwitha"subscript"ofrow,column:

RowsandColumns

Sowhichistherowandwhichisthecolumn?

Rowsgoleftright

Columnsgoupdown

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Torememberthatrowscomebeforecolumnsusetheword"arc":

ar,c

Example:

B=

Herearesomesampleentries:

b1,1=6(theentryatrow1,column1is6)

b1,3=24(theentryatrow1,column3is24)

b2,3=8(theentryatrow2,column3is8)

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