Exam Analysis: MAT223 Linear Algebra, Midterm 1
Exam Analysis: MAT223 Linear Algebra, Midterm 1 1) TEST BREAK DOWN: The material covered for midterm 1 can be break down into 4 different topics: 1) Row Reduced Echelon Form (RREF) and solving linear system of equations 2) Elementary matrices 3) Vector space and subspace 4) Span and linear independence. The test is usually 90 minutes, and worth 55 marks. There are usually 50 marks worth of computation questions with a 5 marks worth of proof questions at the end. This midterm, just as most of other midterms and finals in this course, is very computational in nature. Hence, the ability to quickly and correctly perform the fixed steps in solving different types of problem is essential to doing well in this midterm. Furthermore, this course has been coordinated by Prof. Uppal for many consecutive years and has adopted a very rigid test structure and question types, making recent midterms (such as those analyzed below) extremely similar to each other and future midterms. One immediate consequences of this structure is such that one can pull off a high grade by focusing on the steps involved in performing various computation and not necessary focus on the conceptual idea (i.e. the ability to answer proof questions). Nonetheless, one should not disregard learning concepts as that helps you to understand and better perform computations as well as the last proof question. To master this midterm, understanding how to solve a linear system of equation and reduce st nd matrix to RREF is crucial because 1) this topic constitutes the most marks (usually 1 and 2 question) and 2) it is the basis for most of the other topics in linear algebra, meaning that if you have trouble reducing matrix and solving for linear system, you most likely are unable to find elementary matrices, span sets etc. For the detailed importance of each topic, please refer to the question statistics on the next page.
2) TEST STATISTICS Years/Topics
2011 Fall
RREF, Solving linear system of equations Elementary Matrices Vector Space, Subspace Span, Linear Independence
2012 Winter
2012 Fall
Unknown
20
20
20
20
10 10 15
10 10 15
10 15 10
10 25 0
60 50
Marks
40 Span, Linear Independence
30
Vector Space, Subspace Elementary Matrices
20
RREF
10 0 2011 Fall
2012 Winter
2012 Fall
Unknown
MAT 223 Midterm 1 Break down of questions 1) and 2): solving linear system of equations some times with the RREF of the matrix given 3) Rewrite A or in terms of elementary matrices 4) Prove a given space is a subspace 5) Find the span set, check if a vector belong to a span set or check for a linear independence of vectors 6) A proof question based on the concept from either (Vector Space, Subspaces) or (Span, Linear Independence)
2) TEST STATISTICS Years/Topics
2011 Fall
RREF, Solving linear system of equations Elementary Matrices Vector Space, Subspace Span, Linear Independence
2012 Winter
2012 Fall
Unknown
20
20
20
20
10 10 15
10 10 15
10 15 10
10 25 0
60 50
Marks
40 Span, Linear Independence
30
Vector Space, Subspace Elementary Matrices
20
RREF
10 0 2011 Fall
2012 Winter
2012 Fall
Unknown
MAT 223 Midterm 1 Break down of questions 1) and 2): solving linear system of equations some times with the RREF of the matrix given 3) Rewrite A or in terms of elementary matrices 4) Prove a given space is a subspace 5) Find the span set, check if a vector belong to a span set or check for a linear independence of vectors 6) A proof question based on the concept from either (Vector Space, Subspaces) or (Span, Linear Independence)
