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Symmetric Matrices Video Lecture | Mathematics (Maths) Class 12 - JEE

204 videos|288 docs|139 tests

Timeline

00:03 What is a Symmetric Matrix?
01:36 How to check if matrix is symmetric?
02:30 Rectangular Matrix
03:41 Is every square matrix symmetric?
05:15 Symmetric Matrix (Example)
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FAQs on Symmetric Matrices Video Lecture - Mathematics (Maths) Class 12 - JEE

1. What is a symmetric matrix?
Ans. A symmetric matrix is a square matrix that is equal to its transpose. In other words, if we reflect a symmetric matrix along its main diagonal, the matrix remains unchanged.
2. How can we identify if a matrix is symmetric?
Ans. To determine if a matrix is symmetric, we compare its elements with the corresponding elements in the transpose of the matrix. If all the elements are equal, the matrix is symmetric.
3. What are the properties of symmetric matrices?
Ans. Symmetric matrices have several notable properties. Some of them include: - The eigenvalues of a symmetric matrix are always real. - Symmetric matrices can be diagonalized, meaning they can be expressed as a product of a diagonal matrix and its transpose. - The sum or difference of two symmetric matrices is always symmetric.
4. Can a non-square matrix be symmetric?
Ans. No, a non-square matrix cannot be symmetric. Symmetric matrices are always square matrices, which means they have an equal number of rows and columns.
5. How can symmetric matrices be useful in real-world applications?
Ans. Symmetric matrices have various applications in fields such as physics, computer science, and statistics. Some examples include: - In physics, symmetric matrices are used to represent forces and moments in structural analysis. - In computer science, symmetric matrices are employed in graph theory to represent relationships between nodes in a network. - In statistics, symmetric matrices are used in multivariate analysis to study relationships between different variables.
204 videos|288 docs|139 tests

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