Find Pivot Positions and Pivot Columns [[0,1,4],[0,1,6/7]]

Problem

[[0,1,4],[0,1,6/7]]

Solution

1. Identify the first non-zero column from the left. The first column consists of all zeros, so it cannot contain a pivot. The first pivot must be in the second column.

2. Locate the first pivot. The first non-zero entry in the second column is 1 in the first row. This is the first pivot position.

3. Perform row operations to create a zero below the first pivot. Subtract the first row from the second row ((R_2)−(R_1)→(R_2).

[[0,1,4],[0,0,6/7−4]]

4. Simplify the entry in the second row, third column.

6/7−28/7=−22/7

[[0,1,4],[0,0,−22/7]]

5. Identify the second pivot. In the second row, the first non-zero entry is −22/7 in the third column. This is the second pivot position.

6. Determine the pivot columns. The pivots are located in the second and third columns of the matrix.

Final Answer

Pivot Positions: Row 1, Column 2 and Row 2, Column 3; Pivot Columns: Column 2 and Column 3

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