19 October 2012
TOTAL PAGES: 7
COURSE: MATH 1300
MIDTERM #1
Page 1 of 7
TIME: 60 Minutes
NAME: (Print in ink)
STUDENT NUMBER:
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(I understand that cheating is a serious oense)
PLEASE CIRCLE THE NAME OF YOUR INSTRUCTOR:
B. Penfound
L. Che
Properties of Determinants
Textbook: 2.3
GOALS OF THIS CHAPTER
-introduce and prove some properties of the determinant
-understand that we are not able to break apart a sum
-see some quick ways to test if a determinant is equal to zero
DETERMINANT PROPERT
Matrices and Matrix Operations
Textbook: 1.3
GOALS OF THIS CHAPTER
- introduce various matrix operations and properties
- see examples of special types of matrices
- understand how to write a direct proof
- define positive matrix powers
MATRIX ADDITION
De
Gaussian Elimination
Textbook: 1.2
GOALS OF THIS CHAPTER
-define reduced row echelon form (RREF) and row echelon form (REF) of
a matrix
-see the Gaussian elimination method for reducing a matrix to REF
-see the Gauss-Jordan elimination method for reducing
Elementary Matrices and a Method
for Finding the Inverse
Textbook: 1.5
GOALS OF THIS CHAPTER
- see elementary row operation procedure of finding an inverse
- understand and calculate elementary matrices
-express square matrices as a product of elementary
Further Results on Linear
Systems and Invertibility
Textbook: 1.6
GOALS OF THIS CHAPTER
-see how to prove a set of equivalent statements
-introduce the equivalent statements for linear algebra and prove them
THE EQUIVALENT STATEMENTS
When we say that a li
Introduction to Systems of Linear
Equations
Textbook: 1.1
GOALS OF THIS CHAPTER
-define linear system and use the substitution method to solve 2x2
systems
-see the three types of solutions a linear system may have
-understand how to transfer a linear syst
Inverses and Rules of Matrix
Arithmetic
Textbook: 1.4
GOALS OF THIS CHAPTER
- develop notion of matrix inverse
- discuss properties of matrix inverse
- solve matrix equations
MATRIX INVERSES
When dealing with numbers, we have an
understanding of what the
Diagonal, Triangular and
Symmetric Matrices
Textbook: 1.7
GOALS OF THIS CHAPTER
- define diagonal, triangular and symmetric matrices
- see useful properties of these matrices
DIAGONAL MATRICES
Def. - A square matrix is called a diagonal matrix if all entr
Determinants by Row Reduction
Textbook: 2.2
GOALS OF THIS CHAPTER
-understand how elementary row operations affect the determinant of a matrix
-calculate the determinant of triangular matrices
-calculate the determinant of a matrix using elementary row op
Planes and Lines in 3-Space
Textbook: 3.5
GOALS OF THIS CHAPTER
-how to find the vector form, parametric form and symmetric forms of
lines
-how to find the vector form, scalar form and general form of planes
- prove the formula for distance between a poin
Linear Transformations
from Rn to Rm
Textbook: 4.2
GOALS OF THIS CHAPTER
-define a linear transformation between two Euclidean spaces
-calculate the standard matrix of a linear transformation
-see some geometrical linear operators
-understand that composi
Properties of Linear Transformations
Textbook: 4.3
GOALS OF THIS CHAPTER
-determine if a linear transformation is invertible and find the inverse
linear transformation
-see that a standard matrix is determined by standard basis
vectors
-understand what ei
The Cross Product
Textbook: 3.4
GOALS OF THIS CHAPTER
-define and see basic computations with the cross product
-see properties of the cross product
-use the cross product to compute areas and volumes
-use the cross product as a test for co-planarity
CROS
Determinants by Cofactor
Expansion
Textbook: 2.1
GOALS OF THIS CHAPTER
- introduce minors and cofactors of a matrix
-use cofactor expansion to calculate the determinant of any size matrix
- use the 3x3 quick method to calculate the determinant of a 3x3 ma
Dot Product and Projections
Textbook: 3.3
GOALS OF THIS CHAPTER
-introduce the n-space dot product
-understand how the dot product relates to angles
-see the properties of the dot product
-calculate vector projections
-Cauchy-Schwarz and Triangle Inequali
Introduction to Vectors
Norm of a Vector; Vector Arithmetic
Euclidean n-Space
Textbook: 3.1, 3.2, 4.1
GOALS OF THIS CHAPTER
- revisit the idea of a vector and give more detail to this notion
-basic computation with vectors: length, addition, scalar multip