Transpose [[1,-1,1,3],[1,0,3,6],[0,1,-2,-1]]

Problem

[[1,−1,1,3],[1,0,3,6],[0,1,−2,−1]]

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) in the original matrix moves to position (j,i) in the transposed matrix.

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

[[1,−1,1,3],[1,0,3,6],[0,1,−2,−1]]T=[[1,1,0],[−1,0,1],[1,3,−2],[3,6,−1]]

Want more problems? Check here!