Transpose [[5,-3,7,4],[4,-1,2,-7],[1,4,7,0]]

Problem

[[5,−3,7,4],[4,−1,2,−7],[1,4,7,0]]

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. Apply the definition of a transpose. The transpose of a matrix is formed by switching its rows and columns. The element at position (i,j) moves to position (j,i)

3. Rewrite the first row as the first column. The elements $5, -3, 7, 4$ become the first column of the new matrix.

4. Rewrite the second row as the second column. The elements $4, -1, 2, -7$ become the second column of the new matrix.

5. Rewrite the third row as the third column. The elements $1, 4, 7, 0$ become the third column of the new matrix.

6. Verify the dimensions of the resulting matrix. The transposed matrix is a 4×3 matrix.

Final Answer

[[5,−3,7,4],[4,−1,2,−7],[1,4,7,0]]^T=[[5,4,1],[−3,−1,4],[7,2,7],[4,−7,0]]

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