Matrix Determinant Explorer

How to use this applet

1. Select 2 × 2 or 3 × 3.
2. Drag a colored endpoint to change a vector or edit its matrix column. In 3D, drag the background to rotate the view.
3. Drag one vector onto the same line as another or use the slider to align them. Watch the determinant and area or volume.
4. Use Reset to start again.

Hint

Linearly dependent: Vectors are said to be linearly dependent when one vector lies on the same line as another and can be written as a scalar multiple of it, or when one vector can be written as a combination of the others. The determinant of the matrix formed by these vectors is zero.

Linearly independent: Vectors are said to be linearly independent when they do not lie on the same line, none can be written as a combination of the others, and the determinant of the matrix formed by these vectors is nonzero.

Explore & Investigate

1. Drag the blue or orange endpoint to change the shape (or edit the matrix entries). What happens to the area and determinant?
2. Based on your activity in Explore 1 what conclusion can you draw.
3. Drag one vector onto the same line as the other or use the scalar slider and observe what happens to the determinant and area.
4. Based on your investigation in Explore 3 and your understanding of linear dependence and independence, what can you conclude?