Linear Algebra
Linear Operators
Let the linear transformation \( A \) map the vectors \( \vec{v} \) and \( \vec{w} \) as follows:
\[
\begin{aligned}
A\left(\vec{v}\right) &= -\vec{v}-7\vec{w} \\
A\left(\vec{w}\right) &= \vec{v}-2\vec{w} \\
\end{aligned}
\]
What is the image of the vector \( \vec{u}=4\vec{v}-3\vec{w} \)?
\[
\begin{aligned}
A\left(\vec{v}\right) &= -\vec{v}-7\vec{w} \\
A\left(\vec{w}\right) &= \vec{v}-2\vec{w} \\
\end{aligned}
\]
What is the image of the vector \( \vec{u}=4\vec{v}-3\vec{w} \)?
\(A(\vec{u})={}\)\({}\cdot \vec{v}+{}\)\({}\cdot \vec{w}\)
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