Every matrix can be reduced to a row-reduced echelon matrix by a **sequence** of elementary row operations.

### Explanation
The process of transforming a matrix into its row-reduced echelon form (RREF) involves applying three types of elementary row operations repeatedly. These operations are:

1. **Row Switching**: You can swap two rows in the matrix.
2. **Row Multiplication**: You can multiply a row by a non-zero scalar.
3. **Row Addition**: You can add or subtract a multiple of one row to/from another row.

The sequence of these operations systematically simplifies the matrix, working towards achieving a form where each leading entry of a row is 1, and each leading 1 is the only non-zero entry in its column. The end goal is to make the matrix satisfy certain criteria: having leading 1s in each row that shift to the right as you move down the rows, and all rows consisting entirely of zeros are at the bottom of the matrix. By following this procedure accurately, any matrix can be maneuvered into its row-reduced echelon form, which is crucial for solving systems of linear equations, performing linear transformations, and more complex applications in linear algebra.

Question

Every matrix can be reduced to a row-reduced echelon matrix by a **sequence** of elementary row operations.

### Explanation
The process of transforming a matrix into its row-reduced echelon form (RREF) involves applying three types of elementary row operations repeatedly. These operations are:

1. **Row Switching**: You can swap two rows in the matrix.
2. **Row Multiplication**: You can multiply a row by a non-zero scalar.
3. **Row Addition**: You can add or subtract a multiple of one row to/from another row.

The sequence of these operations systematically simplifies the matrix, working towards achieving a form where each leading entry of a row is 1, and each leading 1 is the only non-zero entry in its column. The end goal is to make the matrix satisfy certain criteria: having leading 1s in each row that shift to the right as you move down the rows, and all rows consisting entirely of zeros are at the bottom of the matrix. By following this procedure accurately, any matrix can be maneuvered into its row-reduced echelon form, which is crucial for solving systems of linear equations, performing linear transformations, and more complex applications in linear algebra.

Knowee AI · Accepted Answer

Every matrix can be reduced to a row-reduced echelon matrix by a **sequence** of elementary row operations.

### Explanation
The process of transforming a matrix into its row-reduced echelon form (RREF) involves applying three types of elementary row operations repeatedly. These operations are:

1. **Row Switching**: You can swap two rows in the matrix.
2. **Row Multiplication**: You can multiply a row by a non-zero scalar.
3. **Row Addition**: You can add or subtract a multiple of one row to/from another row.

The sequence of these operations systematically simplifies the matrix, working towards achieving a form where each leading entry of a row is 1, and each leading 1 is the only non-zero entry in its column. The end goal is to make the matrix satisfy certain criteria: having leading 1s in each row that shift to the right as you move down the rows, and all rows consisting entirely of zeros are at the bottom of the matrix. By following this procedure accurately, any matrix can be maneuvered into its row-reduced echelon form, which is crucial for solving systems of linear equations, performing linear transformations, and more complex applications in linear algebra.

Every matrix can be reduced to row-reduced enchlon matrix by a ____of elementary row operations

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