Math Problem Statement

Let a linear map $T:R^2 -> R^3$ defined by $T\begin{pmatrix}2\1\end{pmatrix}=\begin{pmatrix}2\3\-3\end{pmatrix}$, $T\begin{pmatrix}1\2\end{pmatrix}=\begin{pmatrix}-2\4\0\end{pmatrix}$.

Then $T\begin{pmatrix}1\-4\end{pmatrix}$ is equal to a. $\begin{pmatrix}{r}0\4\end{pmatrix}$ b. $\begin{pmatrix}{r}0\4\end{pmatrix}$ c. $\begin{pmatrix}{r}0\4\end{pmatrix}$ d. $\begin{pmatrix}{r}2\0\2\end{pmatrix}$ e. $\begin{pmatrix}{r}2\0\2\end{pmatrix}$

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Transformation
Matrix Operations
System of Linear Equations

Formulas

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Theorems

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Suitable Grade Level

Advanced High School