Clearing a Column, or "Pivoting"

Here is a step-by-step method that gives you the instruction for the row operation you need to obtain a zero in the pivot column.

(1) Next to the row you want to change, write the name of row you need to change on the left, and the pivot row on the right.

    R2R1
    Row to Change
    Pivot Row

(2) Ignoring signs, decide what positive whole number to multiply each row by so that the row you want to change and the pivot row have the same numerical values in the pivot column. In the situation at hand, the pivot column is

    3
    8

so you can accomplish this by multiplying the second row by 3 and the first by 8. Doing so gives the partial row instruction.

    3 R28 R1.

(3) If the two entries in the pivot column have the same sign, insert a minus (), but if they have different signs, insert a plus (+).

    Here, we get the instruction: 3 R2 + 8 R1.

(4) Now replace that row using the instruction.

    This gives
      3
      4
      1
      8
      1
      2
      		3 R2 + 8 R1
      3
      4
      1
      0
      35
      14

Close this window to return to the tutorial.