Create Singular Matrix: To give an example of a singular matrix, we need a matrix that does not have an inverse. A simple way to create a singular matrix is to have at least two rows or columns that are proportional to each other.
Singular Matrix Example: Example of a singular matrix: Let's take a 2×2 matrix where the second row is a multiple of the first row. [1224] This matrix is singular because the determinant is zero (1×4−2×2=0).
Create Symmetric Matrix: To give an example of a symmetric matrix, we need a matrix that is equal to its transpose. This means the element at row i, column j must be the same as the element at row j, column i for all i and j.
Symmetric Matrix Example: Example of a symmetric matrix: Let's take a 2×2 matrix where the elements mirror across the diagonal. 1331 This matrix is symmetric because it's equal to its transpose.
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