Define elementary matrix.
Understand the Problem
The question is asking for a definition of an elementary matrix, which is a key concept in linear algebra. An elementary matrix is derived from the identity matrix by performing a single elementary row operation. These matrices are important in various matrix operations, including finding the inverse of a matrix and solving systems of equations.
Answer
An elementary matrix is a matrix obtained by performing a single elementary row operation on an identity matrix.
The final answer is an elementary matrix is a matrix that can be obtained by performing a single elementary row operation on an identity matrix.
Answer for screen readers
The final answer is an elementary matrix is a matrix that can be obtained by performing a single elementary row operation on an identity matrix.
More Information
Elementary matrices are crucial in linear algebra for performing row operations efficiently, particularly in algorithms for matrix inversion and solving systems of linear equations.
Tips
A common mistake is to confuse elementary matrices with more complex transformations. Always check that the matrix results from just one elementary row operation on the identity matrix.
Sources
- 2.8: Elementary Matrices - Mathematics LibreTexts - math.libretexts.org
- Elementary matrix - StatLect - statlect.com
- Elementary matrix - Wikipedia - en.wikipedia.org
