Transpose [[1,4,1],[1,3,2]]T

Problem

[[1,4,1],[1,3,2]]T

Solution

1. Identify the dimensions of the original matrix. The matrix has 2 rows and 3 columns, making it a 2×3 matrix.

2. Apply the definition of a transpose. The transpose of a matrix is formed by switching its rows and columns. The element at row i and column j moves to row j and column i

3. Rewrite the first row of the original matrix as the first column of the new matrix. The elements 1, 4, 1$ become the first column.

4. Rewrite the second row of the original matrix as the second column of the new matrix. The elements 1, 3, 2$ become the second column.

5. Determine the dimensions of the resulting matrix. The transposed matrix will have 3 rows and 2 columns, making it a 3×2 matrix.

Final Answer

[[1,4,1],[1,3,2]]T=[[1,1],[4,3],[1,2]]

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