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Let T be linear transformation of $R^{3}$ into $R^{2}$ defined by T( x, y, z ) = (2x + y - z, 3x- 2 y + 4z) for all ( x, y, z ) in $R^{3}$. Then the matrix of T relative to the bases $\beta=\left\{\epsilon_{1}=(1,1,1),\epsilon_{2}=(1,1,0),\epsilon_{3}=(1,0,0)\right\}$ and $\delta=\left\{\eta_{1}=(1,3),\eta_{2}=(1,4) \right\}$ is:
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Let T be linear transformation of $R^{3}$ into $R^{2}$ defined by T( x, y, z ) = (2x + y - z, 3x- 2 y + 4z) for all ( x, y, z ) in $R^{3}$. Then
the matrix of T relative to the bases $\beta=\left\{\epsilon_{1}=(1,1,1),\epsilon_{2}=(1,1,0),\epsilon_{3}=(1,0,0)\right\}$ and $\delta=\left\{\eta_{1}=(1,3),\eta_{2}=(1,4) \right\}$ is:
1). $\begin{bmatrix}3 & 11 & 5 \\-1 & -8 & -3 \end{bmatrix}$
2). $\begin{bmatrix}3 & 11 & -5 \\1 & -8 & 3 \end{bmatrix}$
3). $\begin{bmatrix}-3 & 11 & 5 \\1 & 8 & 3 \end{bmatrix}$
4). $\begin{bmatrix}3 & -11 & 5 \\-1 & 8 & 3 \end{bmatrix}$
