6.45.11 The elementary row operations
Adding a row to another row: rowAdd
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.
Input:
rowAdd([[1,2],[3,4]],0,1)
Output:
Multiplying a row by an expression: mRow scale SCALE
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.
Example.
Input:
mRow(12,[[1,2],[3,4]],1)
Output:
The scale command is the same as mRow except that it
takes the arguments in a different order.
SCALE is a synonym for scale.
-
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.
Example.
Input:
scale([[1,2],[3,4]],12,1)
Output:
Adding k times a row to an another row: mRowAdd scaleadd SCALEADD
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.
Example.
Input:
mRowAdd(1.1,[[5,7],[3,4],[1,2]],1,2)
Output:
The scaleadd command is the same as mRowAdd except
that it takes the arguments in a different order.
SCALEADD is a synonym for scaleadd.
-
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.
Example.
Input:
scaleadd([[5,7],[3,4],[1,2]],1.1,1,2)
Output:
Exchanging two rows: rowSwap rowswap swaprow
The rowSwap command switches two rows in a matrix.
rowswap and swaprow are synonyms for rowSwap.
-
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.
Input:
rowSwap([[1,2],[3,4]],0,1)
Output:
Exchanging two columns: colSwap colswap swapcol
The colSwap command switches two columns in a matrix.
colswap and swapcol are synonyms for colSwap.
-
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.
Input:
colSwap([[1,2],[3,4]],0,1)
Output: