In Maple a vector is represented as a one-dimensional array,
and a matrix is represented as a two-dimensional array.
See `?vector` and `?matrix` for detailed help on vectors
and matrices.

In Maple there are many packages for special applications.
The `linalg` package contains many functions from linear algebra
for computing with vectors and matrices.
In order to use a package, you must load the package using the `with`
command, e.g.

You can now use any of the functions listed. The> with(linalg); Warning: new definition for norm Warning: new definition for trace [BlockDiagonal, GramSchmidt, JordanBlock, add, addcol, addrow, adj, adjoint, angle, augment, backsub, band, basis, bezout, charmat, charpoly, col, coldim, colspace, colspan, companion, concat, cond, copyinto, crossprod, curl, definite, delcols, delrows, det, diag, diverge, dotprod, eigenvals, eigenvects, equal, exponential, extend, ffgausselim, fibonacci, frobenius, gausselim, gaussjord, genmatrix, grad, hadamard, hermite, hessian, hilbert, htranspose, ihermite, indexfunc, innerprod, intbasis, inverse, ismith, iszero, jacobian, jordan, kernel, laplacian, leastsqrs, linsolve, matrix, minor, minpoly, mulcol, mulrow, multiply, norm, nullspace, orthog, permanent, pivot, potential, randmatrix, range, rank, row, rowdim, rowspace, rowspan, rref, scalarmul, singularvals, smith, stack, submatrix, subvector, sumbasis, swapcol, swaprow, sylvester, toeplitz, trace, transpose, vandermonde, vecpotent, vectdim, vector]

> A := matrix([[x-1,2,3],[0,x-2,2],[2,1,x-3]]);

> det(A);

> inverse(A);

If you type `?packages` you will get a list of all the known packages
to Maple and what they are. In particular, this includes

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