 
 
 
14.3.11  Elementary row operations
Adding a row to another row.
The rowAdd command adds one row of a matrix to another row.
- 
rowAdd takes three arguments:
- 
A, a matrix.
- n1 and n2, two integers.
 
- rowAdd(A,n1,n2) returns the matrix obtained
by replacing in A, the row of index n2 by the sum of the rows of
index n1 and n2.
Example
| rowAdd([[1,2],[3,4]],0,1) | 
Multiplying a row by an expression.
The mRow,
scale and
SCALE commands multiply
a row of a matrix by an expression.
- 
mRow takes three arguments:
- 
expr, an expression.
- A, a matrix.
- n, an integer.
 
- mRow(expr,A,n) returns the matrix
obtained by replacing in A, the row of index n by the product of
the row of index n by expr.
The scale or SCALE
command is similar to mRow except for a different
order of arguments.
- 
scale takes three arguments:
- 
A, a matrix.
- expr, an expression.
- n, an integer.
 
- scale(A,expr,n) returns the matrix
obtained by replacing in A, the row of index n by the product of
the row of index n by expr.
Examples
| scale([[1,2],[3,4]],12,1) | 
Adding k times a row to another row.
The mRowAdd,
scaleadd and
SCALEADD commands
add a multiple of one row of a matrix to another.
- 
mRowAdd takes four arguments:
- 
k, a real number.
- A, a matrix.
- n1 and n2, two integers.
 
- mRowAdd(k,A,n1,n2) returns the matrix
obtained by replacing in A, the row with index n2 by the sum
of the row with index n2 and k times the row with index n1.
The scaleadd or SCALEADD
command is similar mRowAdd except
for a different order of arguments.
- 
scaleadd takes four arguments:
- 
A, a matrix.
- k, a real number.
- n1 and n2, two integers.
 
- scaleadd(A,k,n1,n2) returns the matrix
obtained by replacing in A, the row with index n2 by the sum
of the row with index n2 and k times the row with index n1.
Examples
| mRowAdd(1.1,[[5,7],[3,4],[1,2]],1,2) | 
| scaleadd([[5,7],[3,4],[1,2]],1.1,1,2) | 
Exchanging two rows.
The rowSwap or
rowswap or
swaprow
command switches two rows in a matrix.
- 
rowSwap takes three arguments:
- 
A, a matrix.
- n1 and n2, integers.
 
- rowSwap(A,n1,n2) returns the matrix obtained
by exchanging in A, the row with index n1 with the row with
index n2.
Example
| rowSwap([[1,2],[3,4]],0,1) | 
Exchanging two columns.
The colSwap or
colswap or
swapcol
command switches two columns in a matrix.
- 
colSwap takes three arguments:
- 
A, a matrix.
- n1 and n2, integers.
 
- colSwap(A,n1,n2) returns the matrix obtained
by exchanging in A, the column with index n1 with the column with
index n2.
Example
| colSwap([[1,2],[3,4]],0,1) | 
 
 
