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11. Berikan contoh matriks singular! 22. Berikan contoh matriks simetri!

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Q. 11. Berikan contoh matriks singular! 22. Berikan contoh matriks simetri!
  1. 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.
  2. Singular Matrix Example: Example of a singular matrix: Let's take a 2×22 \times 2 matrix where the second row is a multiple of the first row. [12 24]\begin{bmatrix} 1 & 2 \ 2 & 4 \end{bmatrix} This matrix is singular because the determinant is zero (1×42×2=01 \times 4 - 2 \times 2 = 0).
  3. 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 ii, column jj must be the same as the element at row jj, column ii for all ii and jj.
  4. Symmetric Matrix Example: Example of a symmetric matrix: Let's take a 2×22 \times 2 matrix where the elements mirror across the diagonal. 13 31\begin{matrix} 1 & 3 \ 3 & 1 \end{matrix} This matrix is symmetric because it's equal to its transpose.

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