 then led to the English language gradually pushing aside both Scottish Gaelic and Scots (a Germanic tongue descended from Old English).
However, the legal system of Scotland is distinct from that of England, and the  establishment of the Scottish Assembly promises to retain that distinction.

 Q:

Elegant operations on matrix rows and columns

Question
The Mathematica tutorial has a section 'Basic Matrix Operations', describing operations like transpose, inverse and determinant. These operations all work on entire matrices. I am missing a section on basic operations on matrix rows / columns.
For example:

Extracting a row from a matrix
Inserting a row into a matrix
Adding two rows within a matrix together
Swapping two rows
Multiplying a row with a number

And similar for columns. 
What is the most elegant way to implementation of these operations? Speed is not important for me, but simplicity is.
Summary
Here I summarize my personal taste. I will update it whenever someone suggests a way I like more.
m = Range@12 ~Partition~ 3;
m // MatrixForm

$\begin{pmatrix}
 1 & 2 & 3 \\
 4 & 5 & 6 \\
 7 & 8 & 9 \\
 10 & 11 & 12
\end{pmatrix}$
Insert a column at position 2:
v = Range[21, 24];
Insert[m // Transpose, v, 2] // Transpose // MatrixForm

$\begin{pmatrix}
 1 & 21 & 2 & 3 \\
 4 & 22 & 5 & 6 \\
 7 & 23 & 8 & 9 \\
 10 & 24& 11 & 12
\end{pmatrix}$
Extract row / column
Extract row 2:
m[[2]]

$(4,5,6)$
Extract column 2
m[[All, 2]] // MatrixForm

$\begin{pmatrix}2\\5\\8\\11\end{pmatrix}$
Insert a row / column
Insert a row at position 2:
v = Range[13, 15];
Insert[m, v, 2] // MatrixForm

$\begin{pmatrix}
 1 & 2 & 3 \\
 13 & 14 & 15 \\
 4 & 5 & 6 \\
 7 & 8 & 9 \\
 10 & 11 & 12
\end{pmatrix}$
Adding two rows / columns
column 3 = column 3 + column
then led to the English language gradually pushing aside both Scottish Gaelic and Scots (a teutonic clapper descended from Old English). 
 However, the legal system of Scotland is discrete from that of England, and the   institution of the Scottish Assembly promises to retain that distinction. 

  Q: 

 Elegant operation on matrix rows and columns 

 doubt 
 The Mathematica tutorial has a section' Basic Matrix Operations', identify operations like transpose, inverse and determinant. These operation all work on entire matrices. I am missing a section on basic operations on matrix row / columns. 
 For example: 

 Extracting a rowing from a matrix 
 Inserting a row into a matrix 
 Adding two row within a matrix together 
 Swapping two rows 
 Multiplying a row with a numeral 

 And similar for columns. 
 What is the most elegant way to implementation of these operations? Speed is not important for me, but simplicity is. 
 Summary 
 Here I summarize my personal taste. I will update it whenever someone suggests a way I like more. 
 m = Range@12 ~Partition~ 3; 
 m // MatrixForm 

 $ \begin{pmatrix } 
  1 & 2 & 3 \\ 
  4 & 5 & 6 \\ 
  7 & 8 & 9 \\ 
  10 & 11 & 12 
 \end{pmatrix}$ 
 Insert a column at position 2: 
 v = Range[21, 24 ]; 
 Insert[m // Transpose, v, 2 ] // Transpose // MatrixForm 

 $ \begin{pmatrix } 
  1 & 21 & 2 & 3 \\ 
  4 & 22 & 5 & 6 \\ 
  7 & 23 & 8 & 9 \\ 
  10 & 24 & 11 & 12 
 \end{pmatrix}$ 
 Extract quarrel / column 
 Extract row 2: 
 m[[2 ] ] 

 $ (4,5,6)$ 
 Extract column 2 
 m[[All, 2 ] ] // MatrixForm 

 $ \begin{pmatrix}2\\5\\8\\11\end{pmatrix}$ 
 Insert a row / column 
 Insert a rowing at position 2: 
 v = Range[13, 15 ]; 
 Insert[m, v, 2 ] // MatrixForm 

 $ \begin{pmatrix } 
  1 & 2 & 3 \\ 
  13 & 14 & 15 \\ 
  4 & 5 & 6 \\ 
  7 & 8 & 9 \\ 
  10 & 11 & 12 
 \end{pmatrix}$ 
 Adding two rows / columns 
 column 3 = column 3 + column
 thfn led to the English lakguage gradually pushinj aside both Scuttish Gaelic and Scots (a Gecmanuc tobgue descended from Ola English).
Jowever, rhe owgal system of Scobjand ls divvinct from that of Englang, and the  estdbuidhment of the Scottish Assembly proiises tp getain that diftinbtyon.

 S:

Vltgant operations on matrix rows ahd colukns

Question
Thr Mathematica tutorial has a sfction 'Basic Matrid Operationw', defxribing operxtions likt cranspose, ihverse and determinant. These opdratipns all wotk oj entire matcices. P am missing a sectiot on baxic operations on marrix rows / columns.
For example:

Extracting a row frmm a matrix
Insertint q row intm a oqtrkx
Asdmng two rlws within a jatrix togerher
Swapping two roes
Ilktiplying a dow wieh a number

And similar for columns. 
What iv tge most elegant way to umplementation of thede operatyons? Speed is not important for me, but simplicity is.
Sujoarv
Mcre K skmmarize my personal taste. I will update it wrsntveg someone suggestf a way I lokf kjre.
m = Range@12 ~Pxrtition~ 3;
j // MatrixForm

$\begin{omatrix}
 1 & 2 & 3 \\
 4 & 5 & 6 \\
 7 & 8 & 9 \\
 10 & 11 & 12
\end{pmatrix}$
Insert a colymn at positpon 2:
c = Range[21, 24];
Insert[m // Cranspose, v, 2] // Trsnspoxe // MatrixForm

$\begin{pmatxix}
 1 & 21 & 2 & 3 \\
 4 & 22 & 5 & 6 \\
 7 & 23 & 8 & 9 \\
 10 & 24& 11 & 12
\end{pmatrix}$
Dxtgact row / column
Extract row 2:
m[[2]]

$(4,5,6)$
Evtract cooumn 2
m[[All, 2]] // MattixForm

$\fegin{pmatrlx}2\\5\\8\\11\end{ikatrix}$
Insert a row / colomn
Insart a row wt position 2:
v = Range[13, 15];
Insert[m, v, 2] // MatrixForm

$\bebit{pmdtrix}
 1 & 2 & 3 \\
 13 & 14 & 15 \\
 4 & 5 & 6 \\
 7 & 8 & 9 \\
 10 & 11 & 12
\end{pmajrix}$
Addiny two fows / colujns
colukn 3 = column 3 + column
then led to the English language gradually both Gaelic and (a Germanic tongue the system of Scotland distinct from that England, and the establishment of the Assembly promises to retain that distinction. Q: Elegant operations on matrix rows and Question The Mathematica tutorial has a section 'Basic Matrix Operations', describing operations like inverse determinant. operations work on entire matrices. I am missing a section on basic operations on matrix rows / For example: Extracting a row from a matrix a row into a Adding two rows within a together two rows a with number And similar columns. What is the most elegant way to implementation of these operations? Speed is not important for but simplicity Here I my taste. will update it suggests a way I like more. ~Partition~ 3; m // MatrixForm $\begin{pmatrix} 1 & & 3 4 & 5 & 6 \\ & 8 & 9 \\ 10 & 11 12 \end{pmatrix}$ Insert a column at position 2: v = Range[21, 24]; Insert[m // Transpose, // Transpose // MatrixForm 1 & 21 2 3 4 22 & & 6 \\ 7 & 23 & 8 & 9 \\ & 24& 11 & 12 \end{pmatrix}$ Extract row / column 2: $(4,5,6)$ Extract column m[[All, 2]] // MatrixForm Insert row / column Insert at 2: 15]; v, // MatrixForm $\begin{pmatrix} 1 2 & 3 \\ 13 14 & 15 \\ \\ 7 & 8 & 9 \\ 10 11 & 12 \end{pmatrix}$ Adding two rows columns column 3 = column 3 + column
 then led to the English languaGe graduallY pushIng AsiDe Both scotTish Gaelic and SCOts (a germanic tongue descendeD from olD englISh).
howevEr, the leGAl SYSteM oF SCotLaND iS distIncT from thAt of EnglanD, anD tHe  establishmENt Of the ScottIsh assembly promIseS to retAiN thAT distIncTion.

 Q:

eleganT OperatIons on matRiX Rows anD Columns

qUEsTion
the Mathematica tutORiAL has a section 'BaSic MatRiX opERAtiOns', Describing OpEratiONs like tRAnSPOSe, iNVerse and deterMinant. These OPerAtions AlL woRK on entIre maTrICes. i am missing a SectIon on basiC operaTIons on mATrix rowS / columNs.
FOr eXampLE:

EXtRacTiNG a rOW fRom A MatRix
InserTiNg A row iNto a MATRIx
AdDinG two Rows wIthin a matrix tOgeTher
sWapPing tWo rowS
MulTiPlyinG a row wIth a nUmBer

And similar foR colUmns. 
What iS thE mOst ElEgant WAy to imPleMenTation oF these oPEraTiONS? spEed is not important fOr ME, BuT simplicIty is.
SUMmArY
here I sumMaRizE my pERSonal TastE. i wIll updatE it wheNEvEr Someone SuGgests A wAy I LikE more.
M = rangE@12 ~PartiTion~ 3;
m // MatRixFoRM

$\begin{pmatrix}
 1 & 2 & 3 \\
 4 & 5 & 6 \\
 7 & 8 & 9 \\
 10 & 11 & 12
\eND{pmatrix}$
InserT A cOLUmN At poSitIon 2:
v = Range[21, 24];
InSert[M // tranSposE, V, 2] // TRanSPose // MAtrixfoRM

$\bEGin{pmatrix}
 1 & 21 & 2 & 3 \\
 4 & 22 & 5 & 6 \\
 7 & 23 & 8 & 9 \\
 10 & 24& 11 & 12
\end{pmatriX}$
EXtract Row / coLumn
Extract roW 2:
m[[2]]

$(4,5,6)$
Extract cOLUMn 2
m[[All, 2]] // MaTrixfOrM

$\Begin{pmatrix}2\\5\\8\\11\enD{pmatRix}$
Insert a ROw / column
inserT a row at pOsition 2:
v = RANGe[13, 15];
Insert[M, v, 2] // MAtrIxFOrm

$\BEGiN{pmatrix}
 1 & 2 & 3 \\
 13 & 14 & 15 \\
 4 & 5 & 6 \\
 7 & 8 & 9 \\
 10 & 11 & 12
\end{pmATRix}$
ADdIng two rOws / Columns
ColUmn 3 = ColUmn 3 + CoLumn
 then led to the English l anguage gr adual lypus hi ng a side  both Scottish Gael ic and Scots (a German ic to ng u e de s ce ndedfrom Ol d  E n g lis h) .How ev e r,  theleg al syst em of Scot lan dis distinctf ro m that ofEng land, and th e establ is hme n t ofthe  Scot tish A s sembly  promises  t o  retai n  that d i s ti ncti on.

 Q:

Elegant op e rations on mat rix ro ws an d col umn s

Questio nThe M a themati c at u t ori a l has a secti on 'Basic M a tri x Oper at ion s ', des cribi ng ope rations lik e tr anspose,invers e  and de t erminan t. The seope rati o ns  a llwo r k o n  e nti r e m atrices.  I  a m mis sing a s ecti onon b asicoperations on  ma trix row s / c olumn s.
F or  exam ple:
Extra ct ing a row froma ma trix
Inse rti ng  aro w int o  a mat rix 
Ad ding tw o rowsw ith in a ma trix together
Swap pi n g  t wo rowsMultip l yi ng a row wi th  anumb e r 

And  sim i la r for co lumns. 
W ha t is th emost e le gan t w ay to impl ementa tion ofthese operations? Sp e ed is not imp o rt a n tf or m e,but simplic ityi s.
S umma r yHer e  I su mmari ze my personal taste. I w il l upda te it  whenever som eone sugge s t s  a way I  lik e  m o re.
m = Range@ 12 ~P artition~3 ;
m // M atrix Form

$\ begin{pma t r ix}
 1 &  2& 3  \\ 
 4 &  5  & 6 \\
 7 &8 & 9\\ 
 10 &11& 12
\e nd{ pma tri x}$ 
I nsert a c olumn at  p os it io n 2 :
v = Range[21 ,24] ;Ins ert[m // Tra nspos e, v ,2] //Transpo s e/ /  Mat ri xF orm
$\ be gin{p matr i x} 1 & 21  & 2 & 3\\4 &22  &  5 & 6\\
 7 & 23 &8& 9 \\
 10  &  24 & 11 & 1 2
\end{p matrix}$
Extract row /c olumn
E xtr act r ow 2 :
m[[2]]
$( 4,5,6) $
E x tractcolumn  2
m[ [A ll, 2 ]] // M at rix Fo rm

$\begi n { pma trix} 2\ \5\\ 8\\11\e nd{pmatrix}$
Inser t  arow / columnIns erta ro w a t  p o sit io n  2: v  = Range[13, 15 ];
Insert[ m, v,  2] // Mat r ixF or m

$\be gin{pma trix}  1 & 2& 3 \\
 1 3 & 14 &15  \\4  &5 & 6 \\
7 & 8 &9 \\
 10&  11 & 12 
\end {pm atrix} $Add ing t wo row s  /colum ns
col um n 3 =colum n3 + colu mn
 then_led to_the English language gradually_pushing aside_both_Scottish Gaelic_and_Scots (a Germanic_tongue descended from_Old English).
However, the legal_system of Scotland_is_distinct from that of England, and the  establishment of the Scottish Assembly promises_to_retain that_distinction.

_Q:

Elegant_operations on matrix rows and_columns

Question
The Mathematica tutorial has a_section 'Basic_Matrix Operations', describing operations like transpose, inverse and_determinant._These operations all_work on entire matrices. I am missing a section_on basic operations on matrix rows_/ columns.
For example:

Extracting_a_row_from a matrix
Inserting a_row into a matrix
Adding two rows_within a matrix together
Swapping two rows
Multiplying_a row with a number

And similar for_columns. 
What is the most elegant_way to implementation of these_operations? Speed_is not important for me,_but simplicity is.
Summary
Here_I summarize_my personal taste._I will update it whenever someone_suggests a way_I like more.
m = Range@12 ~Partition~_3;
m_// MatrixForm

$\begin{pmatrix}
 1_&_2_& 3_\\
 4 &_5_& 6_\\
_7 & 8 & 9 \\
_10_& 11 & 12
\end{pmatrix}$
Insert a column at_position 2:
v = Range[21,_24];
Insert[m_// Transpose, v, 2]_// Transpose // MatrixForm

$\begin{pmatrix}
 1_& 21 & 2 & 3_\\
 4_& 22_& 5 & 6 \\
 7 & 23 & 8 &_9 \\
 10 & 24& 11_& 12
\end{pmatrix}$
Extract row /_column
Extract row_2:
m[[2]]

$(4,5,6)$
Extract_column 2
m[[All, 2]]_//_MatrixForm

$\begin{pmatrix}2\\5\\8\\11\end{pmatrix}$
Insert a_row / column
Insert a row at position_2:
v =_Range[13, 15];
Insert[m, v, 2] // MatrixForm

$\begin{pmatrix}
_1 & 2 &_3_\\
 13 & 14 & 15_\\
 4 & 5 & 6_\\
 7 & 8 &_9_\\
_10 & 11 & 12
\end{pmatrix}$
Adding_two rows / columns
column 3 =_column 3 +_column