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Inverse of a Matrix Video Lecture | Mathematics for Competitive Exams
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FAQs on Inverse of a Matrix Video Lecture - Mathematics for Competitive Exams
| 1. What is the inverse of a matrix? |  |
Ans. The inverse of a matrix is a mathematical operation that produces a new matrix that, when multiplied with the original matrix, yields the identity matrix. It is denoted by matrix^(-1) or matrix inverse.
| 2. How do you find the inverse of a matrix? | |
Ans. To find the inverse of a matrix, you need to follow these steps:
1. Check if the matrix is invertible or non-singular. If the determinant of the matrix is zero, it does not have an inverse.
2. Calculate the determinant of the matrix.
3. Find the adjoint of the matrix by taking the transpose of the matrix of cofactors.
4. Divide the adjoint by the determinant to get the inverse of the matrix.
| 3. What is the significance of the inverse of a matrix? | |
Ans. The inverse of a matrix has several important applications in various fields of mathematics, science, and engineering. Some of its significances include:
- Solving systems of linear equations.
- Finding the solution to matrix equations.
- Determining the rank, eigenvalues, and eigenvectors of a matrix.
- Performing transformations and rotations in computer graphics.
| 4. Can all matrices be inverted? | |
Ans. No, not all matrices can be inverted. Only square matrices that have a non-zero determinant are invertible. If the determinant of a matrix is zero, it is called a singular or non-invertible matrix. In such cases, the matrix does not have an inverse.
| 5. What happens if a matrix does not have an inverse? | |
Ans. If a matrix does not have an inverse, it is called a singular or non-invertible matrix. In this case, it means that the matrix does not have a unique solution for a system of linear equations associated with it. The absence of an inverse may indicate that the equations are dependent or that the system is underdetermined.
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Dec 23, 2024 Last updated |
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