Maple is a computer algebra system, which was first developed in 1980 at the University of Waterloo in Canada.Maple can handle numerical, symbolic, and graphical representations. Exposure to this type of technology is a course goal of Linear Algebra (and Calculus I with Analytic Geometry).Execute the commands by hitting return anywhere in each line:with(LinearAlgebra): with(plots):M:=Matrix([[1,4],[2,5],[3,6]]);Column Space of MFinding the pivots for a basis for the column space. The pivot columns are the basis and the span of them is the entire column space.GaussianElimination(M);Finding an equation that represents the column space as the vectors in 3-space that are spanned by the column vector. We use a generic vector in the equal column and see when the system is consistent.AugmentedMcolumnspace:=Matrix([[1,4,b1],[2,5,b2],[3,6,b3]]);GaussianElimination(AugmentedMcolumnspace);Plotting the columns to see the space they lie inside ofgraph1:=spacecurve({[t, 2*t, 3*t, t = 0 .. 1]}, color = "Niagara Azure", thickness = 3):
graph2:=textplot3d([1, 2, 3, ` vector [1,2,3]`], color = black):
graph3:=spacecurve({[4*t,5*t,6*t,t = 0 .. 1]}, color = "Spring Orange", thickness = 4, linestyle=Dot):
graph4:=textplot3d([4, 5, 6, ` vector [4,5,6]`], color = black):
display(graph1,graph2,graph3,graph4);Nullspace of MSolve Mx=0. The solutions give the nullspace.AugmentedMnullspace:=Matrix([[1,4,0],[2,5,0],[3,6,0]]);ReducedRowEchelonForm(AugmentedMnullspace);JSFH