Transpose

Problem

[[5,7,0,−3],[5,x,65,x],[−2,−1,1,0],[0,−2,0,34]]

Solution

1. Identify the rows and columns of the given 4×4 matrix.

2. Apply the definition of a transpose, which involves swapping the row indices with the column indices ((A_i*j)T=(A_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. Rewrite the fourth row of the original matrix as the fourth column of the new matrix.

Final Answer

[[5,7,0,−3],[5,x,65,x],[−2,−1,1,0],[0,−2,0,34]]T=[[5,5,−2,0],[7,x,−1,−2],[0,65,1,0],[−3,x,0,34]]

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