SysSolve
Solves a system of linear equations.
Syntax

SysSolve(A)

A
is ann×(n+1)
matrix


SysSolve(A, y)

A
is ann×n
matrix 
v
is ann
dimensional vector

Description
If A
is a nonsingular n×n
matrix and y
an n
dimensional vector, then SysSolve(A, y)
returns the unique n
dimensional vector x
such that A⋅x = y
. If A
is nonsquare or singular or if y
is of the wrong dimension, an error is generated.
SysSolve(A)
is defined as SysSolve(lessen(A), last(cols(A)))
. Equivalently, SysSolve(A, y)
is the same as SysSolve(aug(A, y))
.
x
can also be obtained as A^−1 ⋅ y
or inv(A)⋅y
.
Examples
A ≔ ❨❨5, 0, 1, 2, 5❩, ❨0, 1, 3, 2, 8❩, ❨4, 2, 6, 3, 9❩, ❨1, 2, 0, 5, 3❩, ❨5, 4, 7, 0, 1❩❩
⎛5 0 1 2 5⎞ ⎜0 1 3 2 8⎟ ⎜4 2 6 3 9⎟ ⎜1 2 0 5 3⎟ ⎝5 4 7 0 1⎠
y ≔ ❨19, 17, 34, 12, 29❩
⎛19⎞ ⎜17⎟ e⎜34⎟ ⎜12⎟ ⎝29⎠
x ≔ SysSolve(A, y)
⎛2⎞ ⎜1⎟ e⎜2⎟ ⎜1⎟ ⎝1⎠
A⋅x
⎛19⎞ ⎜17⎟ e⎜34⎟ ⎜12⎟ ⎝29⎠
A^−1 ⋅ y
⎛2⎞ ⎜1⎟ e⎜2⎟ ⎜1⎟ ⎝1⎠