Linear Algebra lab

Exact arithmetic (fractions, no rounding) with every step shown. Each tool solves the same problem by several methods — Gauss and Gauss–Jordan elimination, Cramer's rule, the inverse matrix, LU factorisation, Jacobi and Gauss–Seidel iteration; row reduction, cofactor expansion and Sarrus for determinants; Gauss–Jordan and adjugate for inverses — and checks that they agree. There is also a scanner for systems with a parameter k (like question 1(b) and 2(a) of the finals), eigen-tools, orthogonal tools, matrices relative to bases and a Jacobian-matrix tool (an extension beyond MAT1.002: the Jacobian is the matrix of the linear map that best approximates a function near a point).

Enter matrices with one row per line and entries separated by spaces (fractions like 3/4 are fine). The lab is a checking aid: in the exam there is no calculator, so always practise the hand computation first.