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.

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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.
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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.
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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.
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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.

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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.
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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.
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