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 .

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.