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Linear Algebra: Determinants Video Lecture | Question Bank for GATE Computer Science Engineering - Computer Science Engineering (CSE)
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FAQs on Linear Algebra: Determinants Video Lecture - Question Bank for GATE Computer Science Engineering - Computer Science Engineering (CSE)
| 1. What is the importance of determinants in linear algebra? |  |
Ans. Determinants play a crucial role in linear algebra as they provide information about the properties of a matrix. They can be used to determine if a matrix is invertible, calculate the volume of a parallelepiped formed by vectors, find the solutions of a system of linear equations, and determine the eigenvalues and eigenvectors of a matrix.
| 2. How can determinants be computed in computer science engineering? | |
Ans. Determinants can be computed using various methods in computer science engineering. One common approach is to use the cofactor expansion method, where the determinant of an n x n matrix is calculated by recursively computing the determinants of its (n-1) x (n-1) submatrices. Another approach is to use Gaussian elimination to transform the matrix into an upper triangular form and then multiply the diagonal elements to get the determinant.
| 3. Can determinants be used to solve systems of linear equations? | |
Ans. Yes, determinants can be used to solve systems of linear equations. By representing the system of equations in matrix form, we can use determinants to determine if the system has a unique solution, no solution, or infinitely many solutions. If the determinant of the coefficient matrix is non-zero, the system has a unique solution. If the determinant is zero, the system either has no solution or infinitely many solutions depending on other conditions.
| 4. Are determinants used in computer graphics and computer vision? | |
Ans. Yes, determinants are widely used in computer graphics and computer vision. In computer graphics, determinants are used to calculate the area of polygons, find the intersection of lines and planes, and perform transformations such as scaling and shearing. In computer vision, determinants are used for image registration, feature detection, and 3D reconstruction.
| 5. How can determinants be used to find eigenvalues and eigenvectors of a matrix? | |
Ans. Determinants are used to find eigenvalues and eigenvectors of a matrix by solving the characteristic equation. The characteristic equation is obtained by setting the determinant of the matrix minus a scalar multiple of the identity matrix equal to zero. The roots of the characteristic equation are the eigenvalues of the matrix. Once the eigenvalues are found, the corresponding eigenvectors can be determined by solving a system of linear equations.
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Dec 25, 2024 Last updated |
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