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For the matrix [A] given below, the transpose is _______. [A] = [ [2 3 4], [1 4 5], [4 3 2] ]

1. [ [2 1 4], [3 4 3], [4 5 2] ]
2. [ [4 3 2], [5 4 1], [2 3 4] ]
3. [ [4 2 3], [5 1 4], [2 4 3] ]
4. [ [2 3 4], [1 4 5], [4 3 2] ]

Correct answer: [ [2 1 4], [3 4 3], [4 5 2] ]

Solution

The transpose of a matrix is obtained by swapping its rows and columns. In this case, the first row [2, 3, 4] becomes the first column, the second row [1, 4, 5] becomes the second column, and the third row [4, 3, 2] becomes the third column, resulting in the correct option.

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