Skip to main content\(\newcommand{\avec}{{\mathbf a}}
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\)
An interactive diagram for exploring the determinant of
\(2\times2\) matrices. Across the top, there is a
\(2\times2\) array of sliders that enable the reader to define a
\(2\times2\) matrix.
Below the array of sliders is a set of coordinate axes and the two vectors defined as the columns of the matrix. The parallelogram formed by this pair of vectors is also shaded blue if the vectors are positively oriented and red if negative oriented. The grid of parallel lines formed by the linear combinations of the vectors is also shown.
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 two vectors representing the columns of the matrix, along with the parallelograms they define, are shown below.
