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linalg(deprecated)[backsub] - back substitution on a matrix

Calling Sequence

backsub(U)

backsub(U, b, v)

Parameters

U

-

row reduced matrix

b

-

vector or matrix

v

-

(optional) name

Description

• 

Important: The linalg package has been deprecated. Use the superseding packages, LinearAlgebra and VectorCalculus, instead.

  

- For information on migrating linalg code to the new packages, see examples/LinearAlgebraMigration.

• 

backsub generates a solution vector x to the equation Ux=b.

• 

If b is omitted, or b is 'false' then U is assumed to be an augmented matrix and the last column of U is used in place of b.

• 

If b is a matrix, then x (the solution) will also be a matrix with the same number of columns.

• 

If U is the result of applying forward Gaussian elimination to the augmented matrix of a system of linear equations, as might be obtained from gausselim or gaussjord, backsub completes the solution by back substitution.  If a solution exists, it is returned as a vector.  If no solution exists, an error will be generated.

• 

If the solution is not unique, it will be parameterized in terms of the symbols v[1], v[2], ..., etc. or v[1,k],v[2,k], ... as in the case where b is a matrix. If the third argument v is not specified, the global variable _t will be used.

• 

The input matrix must be in row-echelon form with all zero rows grouped at bottom. Such a matrix is produced by applying gausselim or gaussjord to the augmented matrix of a system of linear equations or by obtaining the LU decomposition.

• 

The command with(linalg,backsub) allows the use of the abbreviated form of this command.

Examples

Important: The linalg package has been deprecated. Use the superseding packages, LinearAlgebra and VectorCalculus, instead.

withlinalg:

A:=randmatrix3,4:

F:=gausselimA

F:=722559401522747857861270056633152256043761

(1)

backsubF

1980256633319375663311208656633

(2)

H:=123213110:

v:=121:

A:=augmentH,v

A:=123121321101

(3)

F:=gaussjordA

F:=101101100000

(4)

backsubF

1_t1_t1_t1

(5)

backsubF,false,x

1x1x1x1

(6)

u:=LUdecompH,L='l'

u:=123033000

(7)

e:=forwardsubl,v

e:=100

(8)

f:=backsubu,e,'s'

f:=1s1s1s1

(9)

evalml &* u &* fv

000

(10)

See Also

linalg(deprecated)[forwardsub], linalg(deprecated)[gausselim], linalg(deprecated)[gaussjord], linalg(deprecated)[linsolve], linalg(deprecated)[LUdecomp], LinearAlgebra


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