Transpose

Problem

[[5,−2,−4],[3,3,2],[−2,5,3]]

Solution

1. Identify the matrix to be transposed. The task provides a system of linear expressions or coefficients which can be represented as a 3×3 matrix A

A=[[5,−2,−4],[3,3,2],[−2,5,3]]

2. Apply the definition of a transpose, which involves swapping the rows and columns of the matrix. The element at row i and column j moves to row j and column i

(A_i*j)T=(A_j*i)

3. Rewrite the first row of the original matrix as the first column of the new matrix.

[[5],[−2],[−4]]

4. Rewrite the second row of the original matrix as the second column of the new matrix.

[[3],[3],[2]]

5. Rewrite the third row of the original matrix as the third column of the new matrix.

[[−2],[5],[3]]

6. Combine these columns to form the transposed matrix AT

Final Answer

[[5,−2,−4],[3,3,2],[−2,5,3]]T=[[5,3,−2],[−2,3,5],[−4,2,3]]

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