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Linsolve - inert matrix solve
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Calling Sequence
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Linsolve(A, b) mod n
Linsolve(A, b, 'r', 't') mod n
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Parameters
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A
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rectangular Matrix
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b
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Vector
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'r'
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(optional) name
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't'
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(optional) name
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n
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an integer, the modulus
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Description
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The Linsolve function is a placeholder for representing the solution x to the linear system  .
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If an optional third parameter r is specified, and it is a name, it is assigned the rank of the matrix A.
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A linear system with an infinite set of solutions will be parameterized in terms of variables. Maple uses the global names _t[1], _t[2], ... are used by default. If an optional fourth parameter t is specified, and it is a name, the names t[1], t[2], etc. will be used instead.
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Examples
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![A := Matrix([[1, 2, 3], [1, 3, 0], [1, 4, 3]])](/support/helpjp/helpview.aspx?si=5704/file00096/math141.png)
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| (1) |
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![b := Vector([1, 2, 3])](/support/helpjp/helpview.aspx?si=5704/file00096/math148.png)
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](/support/helpjp/helpview.aspx?si=5704/file00096/math151.png)
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](/support/helpjp/helpview.aspx?si=5704/file00096/math158.png)
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](/support/helpjp/helpview.aspx?si=5704/file00096/math165.png)
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](/support/helpjp/helpview.aspx?si=5704/file00096/math172.png)
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| (6) |
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](/support/helpjp/helpview.aspx?si=5704/file00096/math186.png)
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An example using GF(2^4).
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![A := Matrix([[1, a, a^2], [1, a^2, 1], [1, a^3, a^2]])](/support/helpjp/helpview.aspx?si=5704/file00096/math198.png)
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| (8) |
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![b := Vector([1, a, a^2])](/support/helpjp/helpview.aspx?si=5704/file00096/math205.png)
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](/support/helpjp/helpview.aspx?si=5704/file00096/math208.png)
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](/support/helpjp/helpview.aspx?si=5704/file00096/math215.png)
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](/support/helpjp/helpview.aspx?si=5704/file00096/math222.png)
| (11) |
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![[0, 0, 0]](/support/helpjp/helpview.aspx?si=5704/file00096/math229.png)
| (12) |
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