Matrices

GeoGebra also supports matrices, which are represented as a list of lists that contain the rows of the matrix.

Example: In GeoGebra, {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}} represents a 3x3 matrix.

In order to display nicely a matrix in the Graphic View, using LaTeX formatting, use FormulaText command.

Example: In the input bar type FormulaText[{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}] to display the matrix using LaTeX formatting.

Matrix Operations

Addition and subtraction examples

• Matrix1 + Matrix2: Adds the corresponding elements of two compatible matrices.
• Matrix1 – Matrix2: Subtracts the corresponding elements of two compatible matrices.

Multiplication examples

• Matrix * Number: Multiplies every element of the matrix by the given number.
• Matrix1 * Matrix2: Uses matrix multiplication to calculate the resulting matrix.

Note: The rows of the first and columns of the second matrix need to have the same number of elements.

Example: {{1, 2}, {3, 4}, {5, 6}} * {{1, 2, 3}, {4, 5, 6}} gives you the matrix {{9, 12, 15}, {19, 26, 33}, {29, 40, 51}}.

• 2x2 Matrix * Point (or Vector): Multiplies the matrix with the given point/vector and gives you a point as a result.

Example: {{1, 2}, {3, 4}} * (3, 4) gives you the point A = (11, 25).

• 3x3 Matrix * Point (or Vector): Multiplies the matrix with the given point/vector and gives you a point as a result.

Example: {{1, 2, 3}, {4, 5, 6}, {0, 0, 1}} * (1, 2) gives you the point A = (8, 20).

Note: This is a special case for affine transformations where homogeneous coordinates are used: (x, y, 1) for a point and (x, y, 0) for a vector. This example is therefore equivalent to: {{1, 2, 3}, {4, 5, 6}, {0, 0, 1}} * {1, 2, 1}.

Other examples

see also section Matrix Commands

• Determinant[Matrix]: Calculates the determinant for the given matrix.
• Invert[Matrix]: Inverts the given matrix
• Transpose[Matrix]: Transposes the given matrix
• ApplyMatrix[Matrix,Object]: Apply affine transform given by matrix on object.
• ReducedRowEchelonForm[Matrix]: Converts the matrix to a reduced row-echelon form