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