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A zero determinant implies that the columns are linearly dependent, causing the transformation to collapse the space into a lower dimension. In 2D, the plane collapses to a line or point; in 3D, it collapses to a plane, line, or point, resulting in zero volume.

Conditions: Square matrix; $\det(M) = 0$

A zero determinant implies that the columns are linearly dependent, causing the transformation to collapse the space into a lower dimension. In 2D, the plane collapses to a line or point; in 3D, it collapses to a plane, line, or point, resulting in zero volume.

Conditions: Square matrix; $\det(M) = 0$

If the columns of a transformation matrix are linearly dependent, it means the transformation collapses the space into a lower dimension. For example, a 2D plane might be squashed into a 1D line or a single point.

Conditions: The matrix represents a linear transformation.; Columns are linearly dependent.

If the columns of a transformation matrix are linearly dependent, it means the transformation collapses the space into a lower dimension. For example, a 2D plane might be squashed into a 1D line or a single point.

Conditions: The matrix represents a linear transformation.; Columns are linearly dependent.