MAT223, Winter 2020: Letter Formed Essay Reflection

This assignment is a letter-formed essay written by a student for the MAT223 course, focusing on linear algebra. The student reflects on their learning experience, addressing concepts such as row-reduction, matrix equations, spans, linear independence, and eigenvectors. The essay is written to an audience familiar with technical math and science, explaining the level of achievement in understanding the course's learning outcomes. The student provides specific examples and anecdotes to illustrate their comprehension of the material, highlighting the practical applications and insights gained throughout the semester. The essay covers topics including set notations, matrices, linear combinations, and the significance of eigenvectors and diagonalization in understanding explicit matrices. The student concludes by expressing the course's impact on their knowledge and understanding of various aspects within linear algebra.

Running head: LETTER FORMED ESSAY 1
Letter Formed Essay
Name of the student
Institution Affiliation

LETTER FORMED ESSAY 2
Letter Formed Essay
Dear uncle,
This year at the university, I have had an exciting experience, and I had gained a lot of
insight into technical staff just like you back in the days when you were in college. This semester
we have taken MAT223, which is a course focusing on row-reduction, matrix equations, spans,
and linear independence, and eigenvectors and diagonalization. Fascinatingly, these concepts are
more impressive than they have ever been because I have managed not only to understand them
but also to gain an understanding of how I can apply them in real life.
In raw reduction, we have learned various basic concepts starting with the basic math
notations such as those of sets, subsets, intersections, unions and also the special sets like N, R, Z
, and Q. Understanding these basic math notations did not seem very useful to me until I created
matrices from different sets when I was exploiting raw reduction techniques. In matrix equations,
it was fascinating to learn that with the help of coefficient matrices, it is possible to have a single
matrix equation from systems of linear equations. If you can recall a single matrix equation is a
matrix equation which takes the form Bx=C where B is expressed as m × n, x is a vector that has
unknown coefficients, and c is a vector in R m.
I understand that any set of linearly independent vectors has the capacity to span a space
because understand what a linear span and linear independence mean in linear algebra. A Span of
a given set of vectors in a vector space, if you can recall, is the smallest linear subspace that
carries the set into consideration. On the other hand, linear independence in linear algebra is used
to refer to a set of vectors that has at least one of the vectors in the set, which is a linear
combination of the others. I have advanced my knowledge not only in identifying eigenvectors,
2

LETTER FORMED ESSAY 3
eigenspace, eigenvalue, and other aspects related to eigenvectors and diagnolization. Being able
to compute eigenvalues algebraically and geometrically is important because it enhances one's
understanding of explicit matrixes.
In conclusion, the course has been fun and highly instrumental. It has expanded my
knowledge and granted me an understanding of various aspects. I hope that I will find an
opportunity to visit and share the rest of the interesting things that we learned in the course.
Yours sincerely
Signature
Name
3