What is a singular matrix?
Understand the Problem
The question is asking about the concept of a singular matrix, which is a term used in linear algebra. A singular matrix is a square matrix that does not have an inverse, typically because its determinant is zero. This indicates that the rows or columns of the matrix are linearly dependent.
Answer
A singular matrix is a square matrix with a determinant of zero.
A singular matrix is a square matrix with a determinant of zero, meaning it is non-invertible and does not have an inverse.
Answer for screen readers
A singular matrix is a square matrix with a determinant of zero, meaning it is non-invertible and does not have an inverse.
More Information
Singular matrices cannot be used where an inverse is required. This property can be used in certain applications, like solving systems of linear equations where the determinant's value can determine the number of solutions.
Tips
A common mistake is assuming that a matrix is singular if it just doesn't have full rank. However, it specifically needs to be a square matrix with a zero determinant to be classified as singular.
Sources
- Singular Matrix - Definition, Properties, Examples, Meaning - Cuemath - cuemath.com
- Singular Matrix -- from Wolfram MathWorld - mathworld.wolfram.com
- Singular Matrix (Definition, Types, Properties and Examples) - BYJU'S - byjus.com
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