Given the bases \(\mathcal{B}=\{b_1,b_2\}\) and \(\mathcal{D…

Given the bases \(\mathcal{B}=\{b_1,b_2\}\) and \(\mathcal{D}=\{d_1,d_2\}\), which matrix below is the change of coordinates matrix from \(\mathcal{D}\) to \(\mathcal{B}\) if \(b_1=\begin{bmatrix}1\\2\end{bmatrix}\), \(b_2=\begin{bmatrix}3\\4\end{bmatrix}\), \(d_1=\begin{bmatrix}1\\4\end{bmatrix}\), and \(d_2=\begin{bmatrix}0\\8\end{bmatrix}\)

Which of the following are linear transformations? I) \( T\b…

Which of the following are linear transformations? I) \( T\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}x+3y\\0\end{bmatrix}\)  II) \( T\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}x+y+1\\2x-y\end{bmatrix}\)    III) \(T\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}xy\\2x-y\end{bmatrix}\)