Linear mappings: Linear mappings
Finding the matrix that determines a linear mapping
The linear map \(A \) from \( \mathbb{R}^2 \) into \(\mathbb R^2\) satisfies
\[\begin{aligned}
A\cv{-3\\1} &= \cv{-13\\12}\\
A\cv{0\\1} &= \cv{-1\\3}\tiny{.}
\end{aligned}\]Determine the matrix of \( A\) with respect to the unit vectors.
\[\begin{aligned}
A\cv{-3\\1} &= \cv{-13\\12}\\
A\cv{0\\1} &= \cv{-1\\3}\tiny{.}
\end{aligned}\]Determine the matrix of \( A\) with respect to the unit vectors.
| The matrix of \(A={}\) |
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