Saved Bookmarks
| 1. |
Express the matrix as `A=[(1,3,5),(-6,8,3),(-4,6,5)]` the sum of a symmetric and a skew-symmetric matrix |
|
Answer» `A = [[1,3,5],[-6,8,3],[-4,6,5]]` Symmetric matrix can be given as `(A+A^T)/2`. Skew-symmetric matrix can be given as `(A-A^T)/2`. Here, `A^T = [[1,-6,-4],[3,8,6],[5,3,5]]` `:.` Symmetric matrix `=1/2[[2,-3,1],[-3,16,9],[1,9,10]]` `:.` Skew-symmetric matrix `= 1/2[[0,9,9],[-9,0,-3],[-9,3,0]]` `:. A = 1/2[[2,-3,1],[-3,16,9],[1,9,10]]+1/2[[0,9,9],[-9,0,-3],[-9,3,0]]` |
|