Today in Precalculus class we solved two large 4×4 matrices using the Gauss-Jordan elimination method. This technique gives a solution by manipulating the rows until you reach triangular form. From the triangular form, it is possible to use back substitution to solve for each of the four variables.
But these problems required the solution to be in reduced row echelon form (RRE). RRE requires the leading coefficient to be a one with all entries both above and below the one to be zero. Once this form is completed, the augmented matrix reveals the complete solution. This particular problem came from the MIT OpenCourse in Linear Algebra taught by Dr. Strang.
My students were excited and challenged to work on college level problems involving linear equations with four unknowns. We completed two problems in class as they can take a while to solve. Even though these problems can be solved using a graphing calculator, I find it beneficial for them to do manually as it increases their computational skills and it also helps them to check their work as they go along. The MIT video also stress that the student needs to document and check as they go along.
This particular video from MIT that we watched was done by Dr. Martina Balagovic, who is the teaching assistant for the class. She advises to document each step as the student goes along as this is a good way to catch any mistakes. These problems are highly computational and challenge the students.
My students completed the same problem she did and also continued to RRE form which took about five more steps. Our book didn’t have any 4×4 matrices to solve so I searched the MIT OpenCourseWare for Linear Algebra and found a few good problems.
This unit is part of a much broader linear algebra course that we are learning about. My students find this topic interesting as there are many applications where matrices are useful in solving problems.
Next class, we will be calculating the determinant and finding the inverse of matrices.
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