Transpose [[x,3y,2],[-2x,5y,1]]

Problem

[[x,3*y,2],[−2*x,5*y,1]]

Solution

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

2. Apply the definition of a transpose. To transpose a matrix, the rows of the original matrix become the columns of the new matrix.

3. Rewrite the first row [x,3*y,2] as the first column of the transposed matrix.

4. Rewrite the second row [−2*x,5*y,1] as the second column of the transposed matrix.

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

[[x,3*y,2],[−2*x,5*y,1]]^T=[[x,−2*x],[3*y,5*y],[2,1]]

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