This site contains a tool that uses an entered matrix to generate the dimensions and a basis for each of the four subspaces: column space, null space, row space, and left null space.
Type of Material:
Simulation
Recommended Uses:
This site can be used in class, at home, or for individual and learning.
Technical Requirements:
Any Internet browser equipped with php.
Identify Major Learning Goals:
To develop a better understanding of subspaces related to a given matrix.
Target Student Population:
Students in a Linear Algebra class.
Prerequisite Knowledge or Skills:
Introductory Linear algebra.
Content Quality
Rating:
Strengths:
In linear algebra the concepts of a row-space, column-space, and null-space of a matrix are extremely important by themselves and in relations to other fundamental notions such as the solution structure of a system of linear equations. The tool under review produces the bases to the above mentioned spaces as parts of the same output which allows the user to see several intrinsic connections at once. Its use is straight-forward and intuitive: the user chooses the dimension of the matrix, types entries into the relevant fields, and then clicks on the “Submit” button. The output appears on a new page and consists of the bases for all of the above spaces and their dimensions. The applet also computes the row-echelon form of the original matrix and its rank.
Concerns:
The program changes undefined fractions such as 1/0 to 1 without any warning or error message.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
The applet efficiently carries out a computation which would be hard to do by hand. A user can adjust the dimension of the matrix. Combining (as mentioned above) all the results of different spaces calculations on one page is very helpful in better understanding of underlying concepts.
The applet can be used as an aid to a lecture or as a quick in-class demonstration. A student can repeatedly examine the vector spaces and their dimensions that correspond to the matrix and discover their relationships and properties.
Concerns:
A link to information on the row and column space and their dimensions would be helpful.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
The applet is intuitive and very easy to use. The average user can begin using the applet immediately.
Concerns:
The site could certainly benefit from the presence of basic navigation buttons.
Creative Commons:
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