linalg(deprecated)/linsolve - Maple Help

linalg(deprecated)

 linsolve
 solution of linear equations

 Calling Sequence linsolve(A, b, 'r', v) linsolve(A, B, 'r', v)

Parameters

 A - matrix b - vector B - matrix r - (optional) name v - (optional) name

Description

 • Important: The linalg package has been deprecated. Use the superseding packages LinearAlgebra[LinearSolve], instead.
 - For information on migrating linalg code to the new packages, see examples/LinearAlgebraMigration.
 • The function linsolve(A, b) finds the vector x which satisfies the matrix equation $A\x\=\b$. If A has n rows and m columns, then $\mathrm{vectdim}\left(b\right)$ must be n and $\mathrm{vectdim}\left(x\right)$ will be m, if a solution exists.
 • If $Ax=b$ has no solution or if Maple cannot find a solution, then the null sequence NULL is returned. If $Ax=b$ has many solutions, then the result will use global names (see below) to describe the family of solutions parametrically.
 • The call linsolve(A, B) finds the matrix X which solves the matrix equation $AX=B$ where each column of X satisfies $\mathrm{Acol}\left(X,i\right)=\mathrm{col}\left(B,i\right)$ . If $\mathrm{AX}=B$ has does not have a unique solution, then NULL is returned.
 • The optional third argument is a name which will be assigned the rank of A.
 • The optional fourth argument allows you to specify the seed for the global names used as parameters in a parametric solution.  If there is no fourth argument, the default, then the global names _t[1], _t[2], _t[3], ... will be used in the vector case, _t[1][1], _t[1][2], _t[2][1], ... in the matrix case (where _t[1][i] is used for the first column, _t[2][i] for the second, etc).  This is particularly useful when programming with linsolve.  If you declare v as a local variable and then call linsolve with fourth argument v, the resulting parameters (v[1], v[2], ...) will be local to the procedure.
 • An inert linear solver, Linsolve, is known to the mod function and can be used to solve systems of linear equations (matrix equations) modulo an integer m.
 • The command with(linalg,linsolve) allows the use of the abbreviated form of this command.

Examples

Important: The linalg package has been deprecated. Use the superseding packages LinearAlgebra[LinearSolve], instead.

 > $\mathrm{with}\left(\mathrm{linalg}\right):$
 > $A≔\mathrm{matrix}\left(\left[\left[1,2\right],\left[1,3\right]\right]\right):$
 > $b≔\mathrm{vector}\left(\left[1,-2\right]\right):$
 > $\mathrm{linsolve}\left(A,b\right)$
 $\left[\begin{array}{cc}{7}& {-3}\end{array}\right]$ (1)
 > $B≔\mathrm{matrix}\left(\left[\left[1,1\right],\left[-2,1\right]\right]\right):$
 > $\mathrm{linsolve}\left(A,B\right)$
 $\left[\begin{array}{cc}{7}& {1}\\ {-3}& {0}\end{array}\right]$ (2)
 > $A≔\mathrm{matrix}\left(\left[\left[5,7\right],\left[0,0\right]\right]\right):$
 > $b≔\mathrm{vector}\left(\left[3,0\right]\right):$
 > $\mathrm{linsolve}\left(A,b,'r'\right)$
 $\left[\begin{array}{cc}\frac{{3}}{{5}}{-}\frac{{7}{}{{\mathrm{_t}}}_{{1}}}{{5}}& {{\mathrm{_t}}}_{{1}}\end{array}\right]$ (3)
 > $\mathrm{linsolve}\left(A,b,'r',v\right)$
 $\left[\begin{array}{cc}\frac{{3}}{{5}}{-}\frac{{7}{}{{v}}_{{1}}}{{5}}& {{v}}_{{1}}\end{array}\right]$ (4)
 > $A≔\mathrm{matrix}\left(\left[\left[5,7\right],\left[10,14\right]\right]\right)$
 ${A}{≔}\left[\begin{array}{cc}{5}& {7}\\ {10}& {14}\end{array}\right]$ (5)
 > $B≔\mathrm{matrix}\left(\left[\left[3,0\right],\left[6,0\right]\right]\right)$
 ${B}{≔}\left[\begin{array}{cc}{3}& {0}\\ {6}& {0}\end{array}\right]$ (6)
 > $\mathrm{linsolve}\left(A,B\right)$
 $\left[\begin{array}{cc}\frac{{3}}{{5}}{-}\frac{{7}{}{\left({{\mathrm{_t}}}_{{1}}\right)}_{{1}}}{{5}}& {-}\frac{{7}{}{\left({{\mathrm{_t}}}_{{2}}\right)}_{{1}}}{{5}}\\ {\left({{\mathrm{_t}}}_{{1}}\right)}_{{1}}& {\left({{\mathrm{_t}}}_{{2}}\right)}_{{1}}\end{array}\right]$ (7)