Mathematics Exam > Mathematics Videos > Algebra > Determinant of a Matrix
Determinant of a Matrix Video Lecture | Algebra - Mathematics
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FAQs on Determinant of a Matrix Video Lecture - Algebra - Mathematics
| 1. What is a determinant of a matrix? |  |
Ans. The determinant of a matrix is a scalar value that can be computed for a square matrix. It provides important information about the matrix, such as whether it has an inverse and whether the system of equations represented by the matrix has a unique solution.
| 2. How is the determinant of a matrix calculated? | |
Ans. The determinant of a 2x2 matrix can be calculated by multiplying the values in the main diagonal and subtracting the product of the values in the off-diagonal. For larger matrices, the determinant can be calculated using expansion by minors or row reduction methods.
| 3. What does the determinant of a matrix tell us about the matrix? | |
Ans. The determinant of a matrix provides information about its properties. If the determinant is nonzero, it means the matrix has an inverse. If the determinant is zero, it means the matrix is singular and does not have an inverse. The determinant also gives us the scaling factor when the matrix is used to transform a vector.
| 4. How can the determinant of a matrix be used to solve systems of linear equations? | |
Ans. The determinant of a matrix can be used to determine whether a system of linear equations has a unique solution, no solution, or infinitely many solutions. If the determinant of the coefficient matrix is nonzero, then the system has a unique solution. If the determinant is zero, then the system either has no solution or infinitely many solutions, and further analysis is required.
| 5. Can the determinant of a matrix be negative? | |
Ans. Yes, the determinant of a matrix can be negative. The sign of the determinant depends on the number of row swaps required to transform the matrix to its row-echelon form. If an odd number of row swaps are performed, the determinant will be negative; otherwise, it will be positive.
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Dec 18, 2024 Last updated |
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