Build/Get tranformation matricies

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Description

Recover the history of the row operations that have been performed. This function combines the transformation matricies into a single transformation matrix representing all row operations or may optionally print all the individual operations which have been performed.

Usage

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buildTmat(x, all = FALSE)

## S3 method for class 'trace'
as.matrix(x, ...)

## S3 method for class 'trace'
print(x, ...)

Arguments

x

a matrix A, joined with a vector of constants, b, that has been passed to gaussianElimination or the row operator functions

all

logical; print individual tranformation matricies?

...

additional arguments

Value

the tranformation matrix or a list of individual transformation matricies

See Also

echelon, gaussianElimination

Examples

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A <- matrix(c(2, 1, -1,
             -3, -1, 2,
             -2,  1, 2), 3, 3, byrow=TRUE)
b <- c(8, -11, -3)

# using row operations to reduce below diagonal to 0
Abt <- Ab <- cbind(A, b)
Abt <- rowadd(Abt, 1, 2, 3/2)
Abt <- rowadd(Abt, 1, 3, 1)
Abt <- rowadd(Abt, 2, 3, -4)
Abt

# build T matrix and multiply by original form
(T <- buildTmat(Abt))
T %*% Ab    # same as Abt

# print all transformation matricies
buildTmat(Abt, TRUE)

# invert transformation matrix to reverse operations
inv(T) %*% Abt

# gaussian elimination
(soln <- gaussianElimination(A, b))
T <- buildTmat(soln)
inv(T) %*% soln

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