Find Pivot Positions and Pivot Columns A=[[1,2],[1,3]]

Problem

A=[[1,2],[1,3]]

Solution

1. Identify the initial matrix A and prepare to perform row operations to reach the row echelon form.

A=[[1,2],[1,3]]

2. Eliminate the entry in the first column of the second row by subtracting the first row from the second row ((R_2)←(R_2)−(R_1).

[[1,2],[1−1,3−2]]=[[1,2],[0,1]]

3. Locate the leading entries in the row echelon form, which are the first non-zero entries in each row.

Pivot 1 is at row 1, column 1

Pivot 2 is at row 2, column 2

4. Determine the pivot columns by identifying which columns in the original matrix A correspond to the columns containing the pivots.

Pivot columns are column 1 and column 2

Final Answer

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

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