# matrixGaussianSubstitute

#### Overview

The matrixGaussianSubstitute function returns the M coefficient number vector from a triangulated array representing the solution of a triangulated system of M simultaneous linear equations in M variables.

The input argument {NumMatrix} must be an M by M+1 matrix representing the original independent variable observations with the dependent variable in the last column all having been triangulated via the Gaussian elimination in the form of::

x x x x... x y

0 x x x... x y

0 0 x x... x y

....

0 0 0 0... x y

The output will be the M coefficient number vector representing the solution to the original system of M simultaneous equations in M unknowns.

Usage

The matrixGaussianSubstitute function is a non-destructive function useful when you want to solve a system of M simultaneous equations in M variables from a triangulated matrix. See Sedgewick[2] chap 37.

#### Syntax

Expression: (matrixGaussianSubstitute NumMatrix)

 Argument: Arguments Name Type Description NumMatrix NumMatrix Matrix containing the triangulated original independent and dependent observations

Returns: A new number Vector containing the M coefficients of the solution.

#### Examples

Here are a number of links to Lambda coding examples which contain this instruction in various use cases.

#### Argument Types

Here are the links to the data types of the function arguments.

 NumMatrix

Here are also a number of links to functions having arguments with any of these data types.

 append binaryInsert boolean cdr compareEQ compareLE compareLT compareNE compare cons copy delete dimension display insert inside integer isAtom isBitVector isBoolean isByteVector isChar isCharacter isComplex isDate isDictionary isDirectory isEqual isError isFloatVector isIdentical isInside isIntegerVector isInteger isLambda isMatrix isMember isMoney isNumberMatrix isNumberVector isNumber isObjectVector isObject isPair isPcodeVector isString isStructure isSymbol isText isType isVector length list macroReplace makeGaussianMatrix makeGramMatrix makeQuotedList map mapc matrixGaussianEliminate matrixGaussianSubstitute member money new number offset pair parent parse pointer ref remove resize reverse saveObject setCar setCdr setLastCdr setq sizeof sort string type uniqueInsert vectorFill writelg writeln

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