# Solve

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##### Solve and Display Solutions for Systems of Linear Simultaneous Equations

Solve the equation system $Ax = b$, given the coefficient matrix $A$ and right-hand side vector $b$, using link{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?

...,

arguments to be passed to link{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

gaussianElimination, showEqn inv, solve

• Solve
##### Examples
# NOT RUN {
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
# }

Documentation reproduced from package matlib, version 0.9.2, License: GPL (>= 2)

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