2/ 28/2015 Mat r ices ht tp: //www.mathsi sfun.com/al gebr a/matrix-i ntroduction.ht ml 1/ 5 Matrices A Matrix is an array of numbers: A Matrix (This one has 2 Rows and 3 Columns) We talk about one matrix, or several matrices. There are many things we can do with them ... Adding To add two matrices: add the numbers in the matching positions: These are the calculations: 3+4=7 8+0=8 4+1=5 6-9=-3 The two matrices must be the same size, i.e. the rows must match in size, and the columns must match in size. Example: a matrix with 3 rows and 5 columns can be added to another matrix

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2/28/2015 Matrices

http://www.mathsisfun.com/algebra/matrixintroduction.html 1/5

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
2/28/2015 Matrices

http://www.mathsisfun.com/algebra/matrixintroduction.html 2/5

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
2/28/2015 Matrices

http://www.mathsisfun.com/algebra/matrixintroduction.html 3/5

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.
2/28/2015 Matrices

http://www.mathsisfun.com/algebra/matrixintroduction.html 4/5

AndtherearespecialwaystofindtheInverse...

...learnmoreaboutthe InverseofaMatrix .

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

NotationAmatrixisusuallyshownbyacapitalletter(suchasA,orB)

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

RowsandColumns

Sowhichistherowandwhichisthecolumn?

Rowsgoleftright

Columnsgoupdown
2/28/2015 Matrices

http://www.mathsisfun.com/algebra/matrixintroduction.html 5/5

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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