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

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

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

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

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