Find Pivot Positions and Pivot Columns

Problem

[[1,0,−5,0,−14],[0,1,2,0,−7],[0,0,0,1,7],[0,0,0,0,8]]

Solution

1. Identify the leading entries in each row of the given matrix. A leading entry is the first non-zero element in a row.

2. Locate the pivot positions. In row 1, the leading entry is 1 in column 1. In row 2, the leading entry is 1 in column 2. In row 3, the leading entry is 1 in column 4. In row 4, the leading entry is 8 in column 5.

3. Determine the pivot columns. The columns containing the pivot positions are columns 1, 2, 4, and 5.

4. Verify the row echelon form. The matrix is already in row echelon form because the leading entries move to the right as we go down the rows, and any rows of zeros would be at the bottom.

Final Answer

Pivot Positions: *(1,1),(2,2),(3,4),(4,5)

Pivot Columns: *Columns *1,2,4,5

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