GATE Civil 2025 Set 2 | Question: 1

Question

For the matrix $[A]$ given below, the transpose is $\_\_\_\_\_\_\_\_\_\_\_$
$$[A]=\left[\begin{array}{lll} 2 & 3 & 4 \\ 1 & 4 & 5 \\ 4 & 3 & 2 \end{array}\right]$$

• A. $\left[\begin{array}{lll}2 & 1 & 4 \\ 3 & 4 & 3 \\ 4 & 5 & 2\end{array}\right]$
• B. $\left[\begin{array}{lll}4 & 3 & 2 \\ 5 & 4 & 1 \\ 2 & 3 & 4\end{array}\right]$
• C. $\left[\begin{array}{lll}4 & 2 & 3 \\ 5 & 1 & 4 \\ 2 & 4 & 3\end{array}\right]$
• D. $\left[\begin{array}{lll}2 & 3 & 4 \\ 1 & 4 & 5 \\ 4 & 3 & 2\end{array}\right]$

Answer 1

a

Answer 2

The transpose of a matrix is obtained by interchanging its rows and columns ($a_{ij} \to a_{ji}$).

Given $A = \begin{bmatrix} 2 & 3 & 4 \\ 1 & 4 & 5 \\ 4 & 3 & 2 \end{bmatrix}$
The first row becomes the first column, the second row becomes the second column, and the third row becomes the third column:
\[ A^T = \begin{bmatrix} 2 & 1 & 4 \\ 3 & 4 & 3 \\ 4 & 5 & 2 \end{bmatrix} \]

Option A is correct.