Hello Sun, Just for your reference (and since I don't have too much time right now), first find the eigenvalues of the matrix. Do this by solving (2 - r)(-2 - r) + 5α = 0, the solutions will be your eigenvalues (r = ±√(4-5α) for your reference)...

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I am a patient and experienced male math tutor available immediately with very flexible hours. If you need help in mathematics, from the middle school through the undergraduate level, I offer myself as a competent and knowledgeable tutor to fill your needs.

As a mathematics graduate student, I had several years of experience teaching at the undergraduate level, in courses ranging from basic algebra to first and second semester calculus. I have lectured, written and graded exams, and held dedicated sessions with students needing extra help in math, so I am well-suited to assist you with your studies in mathematics. I have taught summer sessions as well, so I am familiar with the pace and pressures of the compacted curriculum. Additionally, I have experience tutoring students of all backgrounds individually, in most areas of math, including higher level undergraduate courses such as Linear Algebra, Real Analysis, Statistics, Differential Equations, etc., and also high school AP classes.

I have also helped many students, including adults returning to school, in preparing for the mathematics (and even language) portions of the major college entrance exams, including the SAT I and II, ACT, GRE, and GMAT.

My philosophy tends to be rather simple---a student tends to learn best when he/she masters basic concepts and techniques through guided practice and repetition, the subtler points of theory revealing themselves through the solution of problems, rather than through direct statements or lectures.

I live in Raleigh, but can meet anywhere within reasonable distance, including Durham, Cary and even Chapel Hill. Most students prefer to meet at coffee shops and libraries, or at their homes, but I am also willing to tutor from my home, if this is preferable.

Please contact me if interested in hiring me, or with any questions you might have. Please include some specifics about the subjects in which you need help.

My daughter had a six page document to go over for her pre-calculus midterm. Hassan reviewed over half the document in just one session and my daughter did quite well on her exam. Hassan is very efficient with his time. Great tutor!!

Hassan was able to come to our house on very short notice to help with pre-calculus homework problems. He was very patient, drew out the solutions to many of the problems for easier understanding, and was an overall wonderful person to learn from. Thanks!

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I have taught Calculus I and II at the university as a graduate student. This included writing lessons, delivering lectures, writing and grading exams and homework assignments, and providing office hours. I have also tutored extensively in the subjects (Calculus I, II, III and Advanced Calculus; the first two imply AP Calculus) and am thoroughly acquainted with the canon, and the types of material which instructors like to put on exams. Calculus is also one of my absolute favorite subjects to teach, as it often is the entry-point for students to higher-level mathematical ideas, and helping students learn and master these ideas is very satisfying for me.

In my time as an undergraduate, and later as a mathematics graduate student, I have taken and passed courses in ordinary and partial differential equations. Additionally, I have and currently do tutor students in the subject, particularly first courses in differential equations at the undergraduate level. My own philosophy with regard to this material is that concrete mastery of techniques via repetition should be the first goal, as the theory falls into place more neatly once the student has gained confidence computing correctly.

In my time as an undergraduate, and later as a mathematics graduate student, I took and passed courses in number theory, modern algebra, and combinatorics. These constitute, on the whole, branches on the tree for which the Discrete Math course attempts to serve as basic stem. I have and currently do tutor students in the aforementioned courses, particularly first courses at the undergraduate level. My own philosophy with regard to this material is that the student must collect as many basic examples of each type of system/theorem/algorithm as possible, in order to learn to distinguish the rather abstract ideas that arise in such a course. Computation should also be emphasized, as understanding of the abstract will be made easier by confidence manipulating concrete representations of the ideas.

In my time as an undergraduate and thereafter, a graduate student in mathematics, I have taken and passed courses in Linear Algebra. I have also tutored many students not only in this subject, but also in related fields such as Numerical Analysis and Differential Equations. This beautiful subject is best taught, in my opinion, with an emphasis on concrete application and a fair amount of hand computation. But it also serves as a testing ground for more abstract thinking, via proofs of "theoretical" results, as well as being well-suited for cross-disciplinary examples from physics, statistics, finance, and of course, computational programming via Mathematica, Maple, etc.

As a mathematics graduate student, I tutored and taught students at all levels of mathematical maturity and experience. I have prepared many students for the quantitative portions of standardized tests, including the SAT and ACT.

I have experience tailoring lessons to the demands of the contents of these tests, as well as to the relative needs of the individual student. My overall philosophy is based on methodical practice, careful condensation of concrete techniques into general approaches, and finally a study of the tactics best suited to doing well on the test.

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Hello Sun, Just for your reference (and since I don't have too much time right now), first find the eigenvalues of the matrix. Do this by solving (2 - r)(-2 - r) + 5α = 0, the solutions will be your eigenvalues (r = ±√(4-5α) for your reference)...

Hello Sun, What's next is simply to solve the quadratic! So, multiply it out to get r2 -αr + 5 = 0 and use the quadratic formula to find the roots, which will be your eigenvalues. Regards, Hassan H.

Casadi, You have stumbled upon a series that I used to give my students as a fun challenge! If you really are stuck, I'll give the answer below, but don't look if you still want to give it a shot! The first number is 1, so say "one." Now, to form...

**Great exam review!** —
My daughter had a six page document to go over for her pre-calculus midterm. Hassan reviewed over half the document in just one session and my daughter did quite well on her exam. Hassan is very efficient with his time. Great tutor!!
...

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