Transpose

Problem

[[√(,3),7,2,1],[5,9,15,8],[4,6,7,6]]

Solution

1. Identify the dimensions of the original matrix. The given matrix has 3 rows and 4 columns, making it a 3×4 matrix.

2. Understand the transpose operation. Transposing a matrix involves swapping its rows and columns, such that the element at position (i,j) moves to position (j,i)

3. Rewrite the first row of the original matrix as the first column of the new matrix.

4. Rewrite the second row of the original matrix as the second column of the new matrix.

5. Rewrite the third row of the original matrix as the third column of the new matrix.

6. Verify the dimensions of the resulting matrix. The transposed matrix should have 4 rows and 3 columns, making it a 4×3 matrix.

Final Answer

[[√(,3),7,2,1],[5,9,15,8],[4,6,7,6]]^T=[[√(,3),5,4],[7,9,6],[2,15,7],[1,8,6]]

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