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What are Singular and Non Singular Matrices? Video Lecture | Mathematics (Maths) Class 12 - JEE

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FAQs on What are Singular and Non Singular Matrices? Video Lecture - Mathematics (Maths) Class 12 - JEE

1. What is a singular matrix?
A singular matrix is a square matrix that does not have an inverse. In other words, it is not possible to find another matrix that, when multiplied with the singular matrix, gives the identity matrix. Singular matrices have determinant equal to zero.
2. What is a non-singular matrix?
A non-singular matrix, also known as an invertible or non-degenerate matrix, is a square matrix that has an inverse. This means that there exists another matrix that, when multiplied with the non-singular matrix, results in the identity matrix. Non-singular matrices have a non-zero determinant.
3. How can we determine if a matrix is singular or non-singular?
To determine if a matrix is singular or non-singular, we need to calculate its determinant. If the determinant is equal to zero, then the matrix is singular. If the determinant is non-zero, then the matrix is non-singular.
4. What is the significance of singular and non-singular matrices?
Singular matrices are important in various areas of mathematics, such as linear algebra and differential equations, as they represent systems of equations that have no unique solution. Non-singular matrices, on the other hand, are crucial in solving systems of linear equations and finding unique solutions.
5. Can a matrix be both singular and non-singular?
No, a matrix cannot be both singular and non-singular at the same time. The concepts of singular and non-singular are mutually exclusive. A matrix is either singular (determinant equal to zero) or non-singular (determinant non-zero).
204 videos|288 docs|139 tests

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