A matrix is invertible if its determinant is non-zero, and it is skew symmetric if its transpose is equal to the negative of itself.
Yes, you can use elementary row operations to transform the matrix into its reduced row echelon form, which will show whether it is invertible and skew symmetric.
Yes, you can use the Cholesky decomposition method to solve these types of matrices. This involves finding the square root of the matrix and using it to solve for the original matrix.
It is important to remember that multiplying a row or column by a constant in elementary row operations will not change the determinant of the matrix. Also, be careful when using the Cholesky decomposition method as it only works for matrices with positive determinants.
Yes, these types of matrices are commonly used in physics and engineering for modeling and solving systems with symmetries. They are also used in computer graphics and image processing.