Matrix & Vector Operations

Perform matrix multiplications, compute Row Reduced Echelon Form (RREF) step-by-step, or calculate vector cross products.

RREF mode uses numeric Gauss-Jordan elimination on a 3x4 augmented matrix so solution steps are visible.

Augmented Matrix (3×4)

Calculation Summary

Reduced Echelon Output

1
0
-9
2
0
1
4
1
0
0
0
0

Row Operation Steps:

  • Divide Row 1 by 1.00
  • Row 2 = Row 2 - (2.00) * Row 1
  • Row 3 = Row 3 - (1.00) * Row 1
  • Divide Row 2 by 1.00
  • Row 1 = Row 1 - (2.00) * Row 2
  • Row 3 = Row 3 - (2.00) * Row 2

Frequently Asked Questions

What is RREF used for?

Reduced Row Echelon Form (RREF) is a form of an augmented matrix solved via Gaussian elimination. It allows you to directly read the solutions to systems of linear equations.

How does vector cross product work?

The cross product of two 3D vectors A and B produces a third vector perpendicular to both, calculated as Cx = AyBz - AzBy, Cy = AzBx - AxBz, Cz = AxBy - AyBx.

Are the matrix operations limited to 3x3?

This scientific module supports 3x3 dimensions for matrix multiplication, and 3x4 augmented systems for RREF, which cover standard college linear algebra problems.