Transpose [[2,-4,12],[0,6,-12],[1,-2,3]]

Problem

[[2,−4,12],[0,6,−12],[1,−2,3]]

Solution

1. Identify the rows and columns of the original matrix. The first row is [2,−4,12] the second row is [0,6,−12] and the third row is [1,−2,3]

2. Apply the transpose operation by converting each row of the original matrix into a column of the new matrix.

3. Write the first column using the elements of the first row:

[[2],[−4],[12]]

4. Write the second column using the elements of the second row:

[[0],[6],[−12]]

5. Write the third column using the elements of the third row:

[[1],[−2],[3]]

6. Combine these columns into the final transposed matrix.

Final Answer

[[2,−4,12],[0,6,−12],[1,−2,3]]^T=[[2,0,1],[−4,6,−2],[12,−12,3]]

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