Let A be the matrixa) In Maple, the command nullspace (or equivalently, kernel) can be use...

Let A be the matrix

a) In Maple, the command nullspace (or equivalently, kernel) can be used to find a basis for the nullspace of a matrix. (The basis vectors will be given as row vectors instead of column vectors.) Use this command or a corresponding command in an appropriate software package to find a basis for the nullspace of the matrix A.

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b) Bases for the row space of a matrix can be found with Maple by using the gausselim or gaussjord (or equivalently, rref) commands. Such bases may also be found using the rowspace and rowspan commands. Find bases for row space of the matrix A using each of these four Maple commands or corresponding commands in another appropriate software package. If you are using Maple, compare your results obtained with these four different commands.

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c) Bases for the column space of a matrix can be found with Maple by using the gausselim. or gaussjord commands on the transpose of the matrix Such bases may also be found by using the colspace and colspan commands. Find bases for the column space of the matrix A using each of these four methods in Maple or corresponding commands in another appropriate software package. If you are using Maple, compare your results obtained with these four different approaches.