Understanding Linear Algebra

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An interactive diagram in which the reader can select a $2\times2$ matrix $A$ using a set of sliders appearing in a $2\times2$ array across the top. Below that is a $1\times1$ standard coordinate grid and coordinate axes along with a vector $\vvec$ that can be moved by clicking and dragging. The vector $A\vvec$ is also shown.

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Instructions.

The sliders in the diagram below allow you to choose a matrix $A = \begin{bmatrix} a \amp b \\ c \amp d \end{bmatrix}\text{.}$ The vector $\vvec\text{,}$ shaded red, may be moved by clicking in the head of the vector. The vector $A\vvec$ is then shown in outline.

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