North Carolina Central University
Department of Mathematics and Computer Science
Exam #1
MATH 4410 Linear Algebra I
Instructor Dr. G.Melikian
Name - - - - - - - - - - - - - - - Secton #- - - Problem #
Section 1.2
Linear Combinations, Matrix-Vector Products,
and Special Matrices
Def.1. A linear combination of vectors u , u ,., u is a sum of
scalar multiples of these vectors, that is, a vector of the
Section 3.1
Determinants. Cofactor Expansion
Def. 1. Let
be a matrix. The scalar is called the
DETERMINANT of the matrix and denoted by or . So, we
have
.
(1)
Ex. 1. Compute the determinant of the giv
Section 3.2
Properties of Determinants
We need to know how a determinant will behave if we perform a
linear operation with its rows. Row linear operations will be
used to compute any determinant witho
Section 1.3
Systems of Linear Equations
Def. 1. A system of linear equations is a set of m linear
equations in the same n variables, where m and n are positive
integer numbers. Such a system has the f
Section 1.7
Linear Dependence and Linear Independence
Def. 1. A set of vectors u , u ,., u in the space R is called
linearly dependent if there exist scalars c , c , , c , not all
c u c u . c u 0 . We
Section 2.7
Composition and Invertibility of Linear Transformations
Special Transformations
We begin this Section 2.7 with the next useful result.
Proposition 1. The range of a linear transformation
e
Section 2.4
The Inverse of a Matrix
We start to answer the questions: (a) when a matrix has an inverse?
(b) how can we find the inverse of a matrix? Let me remind you the
definition of the inverse of
Section 2.3
Invertibility and Elementary Matrices
Def. 1. An n n matrix A is called invertible if there is an
n n matrix B such that A B I , B A I . At this case matrix B
is called the inverse of A an
Section 2.6
Linear Transformations and Matrices
Def. 1. Let S1 and S 2 be subsets of R n and R m , respectively. A
function f from S1 into S 2 , written f : S1 S 2 , is a rule that
assigns to each vec
Section 4.1
Subspaces
Def. 1. A set W of vectors in R n is called a subspace of R n if
it has the following three properties:
(a) The zero vector 0 belongs to W .
(b) Whenever vectors u and v belong t