Transpose [[2,-1],[-1,8]]

Problem

[[2,−1],[−1,8]]

Solution

1. Identify the matrix elements and their positions. The given matrix is a 2×2 matrix where the first row is (2,−1) and the second row is (−1,8)

2. Apply the definition of a transpose, which involves swapping the rows and columns of the matrix. The element at row i column j moves to row j column i

3. Rewrite the first row of the original matrix as the first column of the new matrix. The values 2 and −1 become the first column.

4. Rewrite the second row of the original matrix as the second column of the new matrix. The values −1 and 8 become the second column.

5. Observe that because the matrix is symmetric (the element at row 1, column 2 is equal to the element at row 2, column 1), the transposed matrix is identical to the original matrix.

Final Answer

[[2,−1],[−1,8]]T=[[2,−1],[−1,8]]

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