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FAQs on Matrices and Determinants - Business Mathematics and Statistics - B Com
| 1. What are matrices and how are they used in mathematics? |  |
Ans. Matrices are rectangular arrays of numbers, symbols, or expressions, arranged in rows and columns. They are used in various fields of mathematics, including algebra, calculus, and statistics, to represent and solve linear equations, perform transformations, and analyze data.
| 2. How do you calculate the determinant of a matrix? | |
Ans. The determinant of a square matrix can be calculated using various methods, such as the rule of Sarrus for 2x2 matrices, or cofactor expansion for larger matrices. For a 2x2 matrix, the determinant is calculated as ad - bc, where the matrix is represented as [[a, b], [c, d]].
| 3. What is the significance of the determinant in linear algebra? | |
Ans. The determinant provides important information about a matrix, such as whether it is invertible (non-singular) or not (singular). A non-zero determinant indicates that the matrix has an inverse, while a determinant of zero implies that the matrix does not have an inverse and its rows (or columns) are linearly dependent.
| 4. Can you explain the properties of determinants? | |
Ans. Determinants have several key properties, including:
1. The determinant of an identity matrix is 1.
2. The determinant changes sign when two rows (or columns) are swapped.
3. If a row (or column) is multiplied by a scalar, the determinant is multiplied by that scalar.
4. The determinant of a triangular matrix (upper or lower) is the product of its diagonal elements.
| 5. What are some applications of matrices and determinants in real life? | |
Ans. Matrices and determinants have numerous applications in various fields, including engineering (for structural analysis), computer graphics (for transformations), economics (for input-output models), and statistics (for multivariate analysis). They are essential tools in optimizing resources and solving complex systems.
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