SysSolve

Solves a system of linear equations.

Syntax

• SysSolve(A)

  • A is an n×(n+1) matrix

• SysSolve(A, y)

  • A is an n×n matrix

  • v is an n-dimensional vector

Description

If A is a non-singular 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 non-square 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⎠

See also

• inv

• ^