Transpose [[6y+4z=12],[3x+3y=9],[2x-3z=10]]

Problem

[[6*y+4*z,12],[3*x+3*y,9],[2*x−3*z,10]]

Solution

1. Identify the dimensions of the original matrix. The given matrix has 3 rows and 2 columns (3×2.

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

3. Construct the new matrix. The first column of the original matrix becomes the first row of the transposed matrix, and the second column becomes the second row.

4. Determine the final dimensions. The transposed matrix will have 2 rows and 3 columns (2×3.

Final Answer

[[6*y+4*z,12],[3*x+3*y,9],[2*x−3*z,10]]T=[[6*y+4*z,3*x+3*y,2*x−3*z],[12,9,10]]

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