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What is Determinant of a Matrix? Video Lecture | Mathematics (Maths) Class 12 - JEE

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FAQs on What is Determinant of a Matrix? Video Lecture - Mathematics (Maths) Class 12 - JEE

1. What is the determinant of a matrix?
The determinant of a matrix is a scalar value that is computed in a specific way using the elements of the matrix. It is a mathematical property that provides important information about the matrix, such as whether it is invertible or singular.
2. How is the determinant of a matrix calculated?
To calculate the determinant of a matrix, you need to follow a specific procedure depending on the size of the matrix. For a 2x2 matrix, you simply subtract the product of the two diagonal elements. For larger matrices, you can use methods such as cofactor expansion, row operations, or using the formula for the determinant of a triangular matrix.
3. What does the determinant of a matrix indicate?
The determinant of a matrix provides valuable information about the matrix. It can determine whether the matrix is invertible or not. A non-zero determinant indicates that the matrix is invertible, while a zero determinant suggests that the matrix is singular and does not have an inverse. Additionally, the determinant can be used to calculate the area or volume of geometric shapes represented by the matrix.
4. Can the determinant of a matrix be negative?
Yes, the determinant of a matrix can be negative. The sign of the determinant depends on the specific properties and arrangement of the elements within the matrix. For example, a reflection or rotation in a coordinate system can result in a negative determinant.
5. How is the determinant of a matrix used in solving systems of linear equations?
The determinant of a matrix is used to determine whether a system of linear equations has a unique solution, no solution, or infinitely many solutions. By setting up the matrix of coefficients and calculating its determinant, you can determine the number of solutions. If the determinant is non-zero, there is a unique solution. If the determinant is zero, there may be no solution or infinitely many solutions, requiring further analysis.
204 videos|288 docs|139 tests

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