Math Problem Statement

Which of the following is Not an elementary row operation? 1. Dividing a row by a nonzero constant. 2. Multiplying a row by a nonzero constant. 3. Adding a multiple of a row to another row. 4. Interchanging two rows.

Solution

The question is asking which of the following is not an elementary row operation.

Elementary row operations consist of three specific actions that can be performed on the rows of a matrix:

  1. Interchanging two rows.
  2. Multiplying a row by a nonzero constant.
  3. Adding a multiple of one row to another row.

However, dividing a row by a constant is not considered an elementary row operation. So, the correct answer would be:

  • Dividing a row by a nonzero constant (This is not an elementary row operation).

Would you like a detailed explanation of elementary row operations, or do you have any other questions?

Here are five related questions for deeper understanding:

  1. What are the main purposes of elementary row operations in linear algebra?
  2. How do elementary row operations affect the determinant of a matrix?
  3. Can a matrix be reduced to its row echelon form using only elementary row operations?
  4. What is the difference between Gaussian elimination and Gauss-Jordan elimination?
  5. Why is multiplying by zero not allowed in elementary row operations?

Tip: Remember that elementary row operations are crucial in solving systems of linear equations and finding inverses of matrices!

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Matrix Operations

Formulas

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Theorems

Elementary Row Operations

Suitable Grade Level

College-level (Linear Algebra)