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Skew Symmetric Matrices Video Lecture | Mathematics (Maths) Class 12 - JEE

204 videos|288 docs|139 tests

Timeline

00:03 Introduction
00:12 Skew-symmetric Matrix
00:43 Transpose of a Matrix
01:06 Negative of a Matrix
03:06 Condition for the matrix to be Skew-symmetric
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FAQs on Skew Symmetric Matrices Video Lecture - Mathematics (Maths) Class 12 - JEE

1. What is a skew symmetric matrix?
Ans. A skew symmetric matrix is a square matrix in which the elements below the main diagonal are the negatives of the corresponding elements above the main diagonal. In other words, the transpose of a skew symmetric matrix is equal to the negation of the original matrix.
2. How can I identify if a matrix is skew symmetric?
Ans. To identify if a matrix is skew symmetric, you need to check if the transpose of the matrix is equal to the negation of the original matrix. If they are equal, then the matrix is skew symmetric.
3. What are the properties of skew symmetric matrices?
Ans. Skew symmetric matrices have several properties, including: - The main diagonal of a skew symmetric matrix is always made up of zeros. - The determinant of a skew symmetric matrix is either zero (when the matrix is not of odd order) or it is a negative square (when the matrix is of odd order). - The sum of two skew symmetric matrices is also a skew symmetric matrix. - A scalar multiple of a skew symmetric matrix is also a skew symmetric matrix.
4. Can a non-square matrix be skew symmetric?
Ans. No, a non-square matrix cannot be skew symmetric. Skew symmetric matrices are defined only for square matrices, which means they have an equal number of rows and columns.
5. How are skew symmetric matrices used in real-life applications?
Ans. Skew symmetric matrices have various applications in real-life scenarios, such as: - Robotics: Skew symmetric matrices are used to represent the cross product of vectors, which is essential in robotics for calculating rotational motion. - Electromagnetics: Skew symmetric matrices are utilized in electromagnetics to describe the relationship between magnetic fields and electric currents. - Computer Graphics: Skew symmetric matrices are employed in computer graphics for animating 3D objects, as they help in representing rotations efficiently.
204 videos|288 docs|139 tests

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