silemus.
← All examples
  1. 23×33\times 3 determinant expansion
  2. 10Eigenvalues of a 3×33\times 3 matrix
  3. 12Eigenvector for eigenvalue 3
  4. 14Inverse of a 2×22\times 2 matrix
  5. 17Solving a 3×33\times 3 linear system
  6. 20System with no solution
  7. 21Singular matrix, det=0
  8. 22Eigenvalue zero of a matrix
  9. 27Null space of a matrix
  10. 37Volume via scalar triple product
  11. 43Characteristic polynomial, 2×22\times 2
  12. 47Orthogonal matrix check
  13. 48Gram-Schmidt second vector
  14. 49Least-squares line fit
  15. 50Coordinates in a new basis
  16. 51Distance point to plane

37Volume via scalar triple product

Find the volume of the parallelepiped spanned by (1, 0, 0), (0, 2, 0) and (1, 1, 3).

Volume is the absolute value of the determinant of the matrix with the three vectors as rows. Expanding along the first row gives det = 1·(2·3−0·1) = 6, so the volume is 6.

How good is this answer?