Find Pivot Positions and Pivot Columns [[1,0,0,2],[0,1,0,-3],[0,0,1,5]]

Problem

[[1,0,0,2],[0,1,0,−3],[0,0,1,5]]

Solution

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

2. Locate the pivot positions. In this matrix, the leading entries are at row 1, column 1; row 2, column 2; and row 3, column 3.

3. Determine the pivot columns. These are the columns that contain the pivot positions.

4. Conclude that columns 1, 2, and 3 are the pivot columns, and the pivot positions are (1,1) (2,2) and (3,3)

Final Answer

Pivot Positions: *(1,1),(2,2),(3,3); Pivot Columns: *1,2,3

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