Linear Algebra I Section E01, E'00		Exercise 1 Exercise 2 Exercise 3 Exercise 4 Exercise 5 Back to Maple Exercises

A. Relevant Maple Commands

All algebraic manipulations with vectors can be performed in Maple with the use of the known command evalm. Checking the equality of the matrix expressions is implemented by the only command

where exp1, exp2 are the algebraic constructions to be compared.

The length of a vector is found by

where vector is some previously specified vector, and N is an integer number equal to the size of the vector.

In order to evaluate the dot product of two vectors, one may use the command

whose structure is clear from the syntax.

Maple allows a user to plot vectors. The convenient way to do this is the use of the command polygonplot3d. Its operation is possible only after loading the graph package plot. For example, in the following command set:

the parameter orig defines the origin, and p specifies the graph that than is displayed. To plot several graphs in the same coordinate axes, instead of p, one may use a vector of elements associated with the graphs, say, [p, r, q].

Do not forget to take a look at the Maple help for more information.

B. Maple Exercises

1. For the vectors u, v, w which elements are u1 = 1, u2 = 3, u3 = 2; v1 = -1, v2 = 1, v3 = 2; w1 = 2, w2 = 1, w3 = -4

1. check the indentities

   (u + v) + w = u + (v + w); and
   10((u + v) = 10u + 10v

2. compute

   |u| + |v|;
   |u + v|; and
   u · v - v · u

3. plot u, v, and w in separate graphs and in the same graph.

2. Use the determinant technique to find a standard form equation for the plane through P(1,2,-3), Q(-2,4,5), and R(3,3,3). Plot the plane.

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Last modified: Mon, June 5, 2000