GATE 2018 | MATHS | Q-50

Question

Let \( M_2(\mathbb{R}) \) be the vector space of all \( 2 \times 2 \) real matrices over the field \( \mathbb{R} \). Define the linear transformation \( S : M_2(\mathbb{R}) \to M_2(\mathbb{R}) \) by \( S(X) = 2X + X^T \), where \( X^T \) denotes the transpose of the matrix \( X \). Then the trace of \( S \) equals________