Question

row reduce the matrix to reduced echelon the pivot positions in the final matrix and in the original matrix,and list the pivot columns.

Answer 1

To row reduce a matrix to reduced echelon form, perform a sequence of row operations until the matrix satisfies certain properties.

Step-by-step explanation:

To row reduce a matrix to reduced echelon form, you perform a sequence of row operations until the matrix satisfies certain properties:

1. The pivot positions in the final matrix consist of a leading 1 followed by zeros in each row.
2. The pivot positions in the original matrix are located in the same columns as the pivot positions in the final matrix.
3. The pivot columns are the columns containing the pivot positions.

To find the reduced echelon form of a matrix, apply row operations such as interchange two rows, multiply a row by a non-zero scalar, and replace one row by the sum of itself and a multiple of another row. Repeat these operations until the desired properties are achieved.