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Symmetric Matrix: A symmetric matrix is a square matrix that is equal to its transpose. In other words, the matrix is symmetrical about its main diagonal. Properties: 1. _Equal to Transpose_: A symmetric matrix is equal to its transpose, i.e., A = A^T. 2. _Symmetrical about Main Diagonal_: The elements of a symmetric matrix are symmetrical ...
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Give 3 by 3 examples (not just the zero matrix) of (a) a diagonal matrix: ai j=0 if i ≠j. (b) a symmetric matrix: ai j=aj i for all i and j. (c) an upper triangular matrix: ai j=0 if i>j. (d) a skew-symmetric matrix: ai j=-aj for all i and j. | Numerade
Give 3 by 3 examples (not just the zero matrix) of (a) a diagonal matrix: ai j=0 if i ≠j. (b) a symmetric matrix: ai j=aj i for all i and j. (c) an upper triangular matrix: ai j=0 if i>j. (d) a skew-symmetric matrix: ai j=-aj for all i and j. | Numerade
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