# buildTmat: Build/Get tranformation matricies In matlib: Matrix Functions for Teaching and Learning Linear Algebra and Multivariate Statistics

## 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

 ```1 2 3 4 5 6 7``` ```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

## Author(s)

Phil Chalmers

`echelon`, `gaussianElimination`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26``` ```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 ```