Solve: Solve and Display Solutions for Systems of Linear...

In matlib: Matrix Functions for Teaching and Learning Linear Algebra and Multivariate Statistics

Solve and Display Solutions for Systems of Linear Simultaneous Equations

Description

Solve the equation system Ax = b, given the coefficient matrix A and right-hand side vector b, using gaussianElimination. Display the solutions using showEqn.

Usage

Solve(
  A,
  b = rep(0, nrow(A)),
  vars,
  verbose = FALSE,
  simplify = TRUE,
  fractions = FALSE,
  ...
)

Arguments

A	the matrix of coefficients of a system of linear equations
b	the vector of constants on the right hand side of the equations. The default is a vector of zeros, giving the homogeneous equations Ax = 0.
vars	a numeric or character vector of names of the variables. If supplied, the length must be equal to the number of unknowns in the equations. The default is paste0("x", 1:ncol(A).
verbose	logical; show the steps of the Gaussian elimination algorithm?
simplify	logical; try to simplify the equations?
fractions	logical; express numbers as rational fractions, using the fractions function; if you require greater accuracy, you can set the cycles (default 10) and/or max.denominator (default 2000) arguments to fractions as a global option, e.g., options(fractions=list(cycles=100, max.denominator=10^4)).
...	arguments to be passed to gaussianElimination and showEqn

Details

This function mimics the base function solve when supplied with two arguments, (A, b), but gives a prettier result, as a set of equations for the solution. The call solve(A) with a single argument overloads this, returning the inverse of the matrix A. For that sense, use the function inv instead.

Value

the function is used primarily for its side effect of printing the solution in a readable form, but it invisibly returns the solution as a character vector

Author(s)

John Fox

See Also

gaussianElimination, showEqn inv, solve

Examples

  A1 <- matrix(c(2, 1, -1,
               -3, -1, 2,
               -2,  1, 2), 3, 3, byrow=TRUE)
  b1 <- c(8, -11, -3)
  Solve(A1, b1) # unique solution

  A2 <- matrix(1:9, 3, 3)
  b2 <- 1:3
  Solve(A2,  b2, fractions=TRUE) # underdetermined

  b3 <- c(1, 2, 4)
  Solve(A2, b3, fractions=TRUE) # overdetermined

matlib documentation built on Nov. 5, 2025, 6:24 p.m.