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Step 1: Two nonparallel lines in space that do not intersect are called Skew lines. Step 2: Among the pairs, the lines and are nonparallel and lie in different planes, and do not intersect each other.. Step 3: So, and are skew lines among the given pairs.
Otherwise, a skew-symmetric matrix is just the same thing as a symmetric matrix. Sums and scalar multiples of skew-symmetric matrices are again skew-symmetric. Hence, the skew-symmetric matrices form a vector space. Its dimension is n (n â1)/2.Let Mat n denote the space of n Ã n matrices.A skew-symmetric matrix is determined by n (n â 1)/2 scalars (the number of entries above the main diagonal); a symmetric matrix is determined by n (n + 1)/2 scalars (the number of entries on or above the main diagonal).ore generally, every complex skew-symmetric matrix can be written in the form A = U Ï U T where U is unitary and Ï has the block-diagonal form given above with complex Î» k. This is an example of the Youla decomposition of a complex square matrix.