Transpose [[x,y,z,6],[x,-y,z,7]]

Problem

[[x,y,z,6],[x,−y,z,7]]

Solution

1. Identify the dimensions of the original matrix. The matrix has 2 rows and 4 columns, making it a 2×4 matrix.

2. Apply the definition of a transpose. The transpose of a matrix is formed by switching its rows and columns. The element at row i and column j moves to row j and column i

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

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

5. Determine the dimensions of the resulting matrix. The transposed matrix will have 4 rows and 2 columns, making it a 4×2 matrix.

Final Answer

[[x,y,z,6],[x,−y,z,7]]T=[[x,x],[y,−y],[z,z],[6,7]]

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