Question
Assume that $T$ defines a linear transformation and use the given information to find the matrixof $T.$$T: \mathbb{R}^{4} \rightarrow \mathbb{R}^{2}$ such that $T(1,0,0,0)=(3,-2)$ $T(1,1,0,0)=(5,1), T(1,1,1,0)=(-1,0),$ and $T(1,1,1,1)=(2,2)$.
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Assume that $T$ defines a linear transformation and use the given information to find the matrix of $T.$ $T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{4}$ such that $T(-1,1)=(1,0,-2,2)$ and $T(1,2)=(-3,1,1,1).$
Linear Transformations
Definition of a Linear Transformation
Assume that $T$ defines a linear transformation and use the given information to find the matrix of $T.$ $$\begin{aligned} &T: \mathbb{R}^{3} \rightarrow \mathbb{R}^{3} \text { such that } T(1,2,0)=(2,-1,1),\\ &T(0,1,1)=(3,-1,-1) \text { and } T(0,2,3)=(6,-5,4) \end{aligned}$$.
Consider the linear transformation $T$ from $\mathbb{R}^{3}$ to $\mathbb{R}^{2}$ with $$T\left[\begin{array}{l} 1 \\ 0 \\ 0 \end{array}\right]=\left[\begin{array}{r} 7 \\ 11 \end{array}\right], \quad T\left[\begin{array}{l} 0 \\ 1 \\ 0 \end{array}\right]=\left[\begin{array}{l} 6 \\ 9 \end{array}\right]$$ and $T\left[\begin{array}{l}0 \\ 0 \\ 1\end{array}\right]=\left[\begin{array}{r}-13 \\ 17\end{array}\right]$ Find the matrix $A$ of $T$
Introduction to Linear Transformations and Their Inverses
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