MAT 260 Linear Algebra-Fall 2012
Worksheet 1 - Review
1. Solve the linear system
x + y=4
3x + 3y = 6
2. Solve the linear system
4x - 2y = 1
16x - 8y = 4
3. Solve the linear system
x + y + 2z = 9
2x + 4y 3z = 1
3x + 6y 5z = 0
4. Figure A shows a network wi
Chapter 2
Determinants by Cofactor Expansion
Evaluating Determinants by Row Reduction
Properties of the Determinants, Cramers Rule
04/12/14
1
Minor and Cofactor
a b
Let A be a 2x2 matrix A =
c d
Then ad-bc is called the determinant of the matrix A, and
1.5 Elementary Matrices and a Method for Finding A1
An elementary row operation on a matrix A is any one of the following three
types of operations:
Interchange of two rows of A.
Replacement of a row r of A by c r for some number c 0.
Replacement of a
1.4 Inverses; Rules of Matrix Arithmetic
For real numbers a and b ,we always have ab = ba, which is called the
commutative law for multiplication. For matrices, however, AB and
BA need not be equal.
Equality can fail to hold for three reasons:
The product
Chapter 1 Systems of Linear Equations and Matrices
Introduction to System of Linear Equations
Gaussian Elimination
Matrices and Matrix Operations
Inverses; Rules of Matrix Arithmetic
Elementary Matrices and a Method for Finding
A 1
Further Results on
1.3 Matrices and Matrix Operations.
A matrix is a rectangular array of numbers. The numbers in the arry are called the
Entries in the matrix.
The size of a matrix is described in terms of number of rows and columns in contains.
A matrix with only one colu
Chapter 3 Euclidean Vector Spaces
Vectors in n-space
Norm, Dot Product, and Distance in n-space
Orthogonality
http:/www.traileraddict.com/clip/despicable-me/vectors-introduction
3. 1 Vectors in n-space
Definition
If n is a positive integer, then an order
Chapter 4 Chapter Content
1. Real Vector Spaces
2. Subspaces
3. Linear Independence
4. Basis
5. Dimension
6. Row Space, Column Space, and Nullspace
8. Rank and Nullity
9. Matrix Transformations for Rn to Rm
Definition (Vector Space)
Let V be an arbitrary