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

This exercise helps you learn how to compute determinants with Maple. It also helps review some of the basic material of the relevenat course topic.

Just a reminder - any Maple work with linear algebra commands starts with loading of linalg package:

Maple alllows to find a minor of a matrix. The syntax of the command is clear from the following example showing how to get the expansion of a 4 x 4 matrix A about the entry in the 4th row and 2nd column:

For finding determinant of a matrix A Maple has a special command:

where A is any square matrix.

Maple allows to determine permutation. In order to get all permutations of {1,...,n}, the command permute can be used. However, first you need to load the package combinat; so there should be the following lines: following:

where n is any positive integer. Maple can also return not all, but a random permutation of {1,2,...,n}. For this purpose, use the command:

B. Maple Exercises

I. Let matrix B be

1. Compute

   (i) det(5B) - 125det(B), and
   (ii) det(B^-1) - 1/det(B).

   Explain your results.
   
   
2. Find det(B) by cofactor expansion about the second column.

II. Let the given system of linear equations is:

-85x - 55y - 37z = -306
-35x + 97y + 50z = 309
-85x - 55y - 37z = 338

Solve the system

(i) by matrix inversion, and
(ii) by Cramer's rule.

III. Find all and one random permutations of {1,2,3,4}. Check that the number of permutations found is thee correct one.

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Last modified: Mon, June 5, 2000