Matrices

The easiest way to create a matrix in GeoGebra is to use the spreadsheet. The matrix

\[\mathbf{A}=\left( \begin{array}{ccc} 1 & 2 & 3 \\ 4 & 5 & 6 \\ \end{array} \right)\]

is entered as in the picture below. Then you select the six cells and choose the spreadsheet tool "Create Matrix".

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In the window that pops up, you can give the matrix a name before clicking on Create.

If you click on the small arrow below the input bar, you can find all commands for vectors and matrices.

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As an example you can create another matrix that is the transpose of \(\mathbf{A}\) by using the command Transpose[A]. The transpose \(\mathbf{A^T}\) of a matrix \(\mathbf{A}\), is the result when swapping the columns and the rows.

\[\mathbf{A^T}=\left( \begin{array}{ccc} 1 & 4 \\ 2 & 5 \\ 3 & 6 \\ \end{array} \right)\]

If you want to use an element of a matrix, you can use the command Element[<matrix>, <row>, <column>]. If you enter Element[A,2,3], 6 is returned.

Points/vectors and matrices in GeoGebra

A vector can be seen as a matrix with one column, a \(m\times 1\) matrix. The vector \(\mathbf{u}\) below is a \(2\times 1\) matrix.

\[\mathbf{u}=\left( \begin{array}{ccc} a \\ b \\ \end{array} \right)\]

A visual point P having the coordinates (a,b) is represented like this P=(a,b) in GeoGebra.

You get the x- and y-coordinate of a point P by writing x(P) and y(P)respectively.

Even though points and vectors/matrices are represented in different ways, you can multiply a matrix with a point.

by Malin Christersson under a Creative Commons Attribution-Noncommercial-Share Alike 2.5 Sweden License

www.malinc.se