How to calculate rank of a matrix in Geogebra

In this lesson you will learn how to calculate the rank of a square matrix in Geogebra.

What is the rank of a matrix? It is the highest order among the square submatrices in the matrix which have a non-zero determinant.

Type in a square matrix.

For example, a 3x3 square root with three rows and three columns.

write a square matrix with 3 rows and 3 columns

Note. If you don't know how to make a matrix, read our lesson on how to make a matrix in Geogebra.

Use the MatrixRank() function to calculate the rank of the matrix.

Write the name of the starting matrix in the round brackets.

matrix rank

Geogebra calculates and displays the rank of the matrix.

Explanation. In this case the rank of the matrix is 2 because the determinant of the 3x3 matrix is zero Δ (m1) = 0. Therefore, the rank cannot be three.
the rank of the matrix is not three
At least one minor 2x2 submatrix has a non-zero determinant. For example, the submatrix in blue has the determinant Δ = -2.
the explanation of the rank calculation
The blue submatrix is of order 2 as it has two rows and two columns. Therefore, the highest order among minors with non-zero determinant is two. Any other submatrixes would have an order equal to or less than the one just found.

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