Function: math[isDependent] - checks whether column vectors are dependent

Calling Sequence:

isDependent(A);
isDependent(v);
isDependent(v1, ..., vk);

Parameters:

A - a matrix
v - a vector
v1, ..., vk - two or more vectors

Description:

In the first form, isDependent checks whether the column vectors in the matrix A are linearly dependent.

In the second form, isDependent checks whether the vector v is linearly dependent.

In the third form, isDependent determines whether the vectors v1, ..., vk are linearly dependent.

In all cases, the return is either true if the objects are linearly dependent, and false otherwise.

This function is part of the math package, and so can be used only after performing the command with(math) or with(math, isDependent).

Examples:

> with(math, isDependent, V, mat): with(linalg, augment, linsolve):

> A := mat(`-2 3 -4 -2; 3 1 1 1, -4 -5 2 0`);

[Maple Math]

> linsolve(A, V(0, 0, 0));

[Maple Math]

> isDependent(A);

[Maple Math]

> isDependent(V(1, 2));

[Maple Math]

> isDependent(V(0, 0, 0));

[Maple Math]

> vs := V(1, -3, 2), V(2, -1, 1), V(4, 3, -1);

[Maple Math]

> linalg[linsolve](augment(vs), V(0, 0, 0));

[Maple Math]

> isDependent(vs);

[Maple Math]

See Also:

Version History:

Version 1.0 - September 13, 1998