Solve
Matrices
Vectors, indexes, and a matrix equation. 3 examples.
v[i] and A[i, j] are 1-based. eye, ones, and zeros build matrices. Indexes start at 1. One index on a whole matrix is an error. inv inverts. transpose swaps the dimensions. There is no transpose operator. A*x = b, with A and b already known, solves the linear system. case is documented under If and case.
Matrix linear solve
One matrix equation.
A Hilbert matrix, built and solved
Each entry is an outer product, summed. The exact solution is the integer vector. d is roundoff: this matrix is badly conditioned.
Cayley–Hamilton
Z is the zero matrix. A 2×2 matrix satisfies its own characteristic equation. The trace and the determinant are read by index.