Midterm Concepts Flashcards
A power series that gives the expansion of a function f (x) in the neighborhood of a point a provided that in the neighborhood the function is continuous, all its derivatives exist, and the series converges to the function.
Taylor Series
Taylor Series is also known as
Taylor Polynomial
is a representation of a function as an infinite sum of terms calculated from the values of its derivatives at a single point.
Taylor Series
is a special case of the Taylor Polynomial, that uses zero as our single point.
Maclaurin Polynomial
The derivative of the function f(x) evaluated at x=a gives the ________ at x=a.
slope of the curve
The integral of the function f(x) over the range x=b to x=c gives the ______ between those points.
area under the curve
In many economic analysis, variables are assumed to be related by sets of
linear equations
provides a clear and concise notation for the formulation and solution of such problems, many of which would be complicated in conventional algebraic notation.
Matrix algebra
The concept of ______ and is based on that of matrix.
determinant
A set of mn numbers (_______), arranged in a rectangular formation (array or table) having m rows and n columns and enclosed by a square bracket [ ] is called m n (‘m by n’) _______
real or complex; matrix
is the ordered pair having as first component the number of rows and as second component the number of columns in the matrix.
Order of a Matrix
In general if m are rows and n are columns of a matrix, then its order is
(m x n)
A matrix consisting of a single row is called a
Rox Matrix or Row Vector
A matrix having single column is called a
Column Matrix or Column Vector
A matrix in which each element is ‘0’ is called a
Null or Zero Matrix
are generally denoted by the symbol O. This distinguishes zero matrix from the real number 0.
Zero Matrices
A matrix A having same numbers of rows and columns is called a
Square Matrix
If m = n, then the matrix is said to be a
Square Matrix
A square matrix of order n x n, is simply written as
An
is the ordered set of elements aij, where i=j extending from the upper left-hand corner to the lower right-hand corner of the matrix.
Principal Diagonal of a Square Matrix
A square matrix in which all elements are zero except those in the main or principal diagonal is called a
Diagonal Matrix
A diagonal matrix in which all the diagonal elements are same, is called a
Scalar Matrix
A scalar matrix in which each diagonal element is 1 (unity) is called a
Identity Matrix or Unit Matrix
An identity matrix of order n is denoted by
In
[aij]mxn is an identity matrix if and only if
aij = 0 and i ≠ j ; aij = 1 for i = j
If a matrix A and identity matrix I are comformable for multiplication, then I has the property that
AI = IA = A
They have the same order and each element of matrix A is equal to the corresponding element of matrix B
Equal Matrices
is the matrix formed by replacing each element in the matrix Amxn with its additive inverse.
The Negative of a Matrix
For every matrix Amxn, the matrix -Amxn has the property that
A + (-A) = (-A) + A = 0
If A is a matrix and k is a scalar (constant), then kA is a matrix whose elements are the elements of A , each multiplied by k
Multiplication of a Matrix by a Scalar
If A and B are two matrices of same order m n then their sum A + B is defined as C, m n matrix such that each element of C is the sum of the corresponding elements of A and B .
Addition and Subtraction of Matrices
Two matrices A and B are said to be conformable for the product AB if the number of columns of A is equal to the number of rows of B.
Product of Matrices
Multiplication of matrices is not
Commutative
A matrix A can be multiplied by itself if and only if it is a
Square Matrix
In the product AB, A is said to be _____ of B and B is said to be _____ of A
pre multiple ; post multiple
True of False: Multiplying the elements of the first row of A by the corresponding elements of the first column of B and adding the product is the right of doing product of matrices.
True
