Transpose [[7,2,2,-2],[-1,0,-1,-1],[4,2,-3,-6]]

Problem

[[7,2,2,−2],[−1,0,−1,−1],[4,2,−3,−6]]T

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

3. Rewrite the first row [7,2,2,−2] as the first column of the new matrix.

4. Rewrite the second row [−1,0,−1,−1] as the second column of the new matrix.

5. Rewrite the third row [4,2,−3,−6] 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

[[7,2,2,−2],[−1,0,−1,−1],[4,2,−3,−6]]T=[[7,−1,4],[2,0,2],[2,−1,−3],[−2,−1,−6]]

Want more problems? Check here!