6.56.5  Step by step Gauss-Jordan reduction of a matrix: pivot

One step of Gauss-Jordan elimination involves taking a non-zero element of a matrix (the pivot) and adding multiples of its row to the other rows to get zeros above and below the pivot. The pivot command performs this operation.

• pivot takes three arguments:
  • A, a a matrix with n rows and p columns.
  • l and c, two integers such that l is the index of a row of A and c is an index of column of A, and the element of A in row l and column c is non-zero.
• pivot(A,l,c) returns the result of performing one step of the Gauss-Jordan method using the element of A in row l, column c as pivot.

Examples.

• Input:
  pivot([[1,2],[3,4],[5,6]],1,1)
  Output:

  ⎡ ⎢ ⎢ ⎣

  −2 0 3 4 2 0

  ⎤ ⎥ ⎥ ⎦

• Input:
  pivot([[1,2],[3,4],[5,6]],0,1)
  Output:

  ⎡ ⎢ ⎢ ⎣

  1 2 2 0 4 0

  ⎤ ⎥ ⎥ ⎦