The matrices $$A_1 = \left[\begin{array}{cc} 1 &0\cr 0 &0 \end{array}\right], \ A_2 = \left[\begin{array}{cc} 0 &1\cr 0 &0 \end{array}\right],$$ $$A_3 = \left[\begin{array}{cc} 0 &0\cr 1 &0 \end{array}\right], \ A_4 = \left[\begin{array}{cc} 0 &0\cr 0 &1 \end{array}\right],$$ form a basis for the linear space $V={\mathbb R}^{2\times 2}.$ Write the matrix of the linear transformation $T:{\mathbb R}^{2\times 2} \rightarrow {\mathbb R}^{2\times 2}$ such that $T(A)=4 A + 10 A^T$ relative to this basis.

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