Linear mappings: Linear mappings
The notion of linear mapping
Let the linear transformation \( A \) map the vectors \( \vec{v} \) and \( \vec{w} \) as follows:
\[
\begin{aligned}
A\left(\vec{v}\right) &= -6\vec{v}+2\vec{w} \\
A\left(\vec{w}\right) &= 9\vec{v}-2\vec{w} \\
\end{aligned}
\]
What is the image of the vector \( \vec{u}=5\vec{v}-\vec{w} \)?
\[
\begin{aligned}
A\left(\vec{v}\right) &= -6\vec{v}+2\vec{w} \\
A\left(\vec{w}\right) &= 9\vec{v}-2\vec{w} \\
\end{aligned}
\]
What is the image of the vector \( \vec{u}=5\vec{v}-\vec{w} \)?
\(A(\vec{u})={}\)\({}\cdot \vec{v}+{}\)\({}\cdot \vec{w}\)
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