Midterm Concepts

Question 1

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.

Answer 1

Taylor Series

Question 2

Taylor Series is also known as

Answer 2

Taylor Polynomial

Question 3

is a representation of a function as an infinite sum of terms calculated from the values of its derivatives at a single point.

Answer 3

Taylor Series

Question 4

is a special case of the Taylor Polynomial, that uses zero as our single point.

Answer 4

Maclaurin Polynomial

Question 5

The derivative of the function f(x) evaluated at x=a gives the ________ at x=a.

Answer 5

slope of the curve

Question 6

The integral of the function f(x) over the range x=b to x=c gives the ______ between those points.

Answer 6

area under the curve

Question 7

In many economic analysis, variables are assumed to be related by sets of

Answer 7

linear equations

Question 8

provides a clear and concise notation for the formulation and solution of such problems, many of which would be complicated in conventional algebraic notation.

Answer 8

Matrix algebra

Question 9

The concept of ______ and is based on that of matrix.

Answer 9

determinant

Question 10

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’) _______

Answer 10

real or complex; matrix

Question 11

is the ordered pair having as first component the number of rows and as second component the number of columns in the matrix.

Answer 11

Order of a Matrix

Question 12

In general if m are rows and n are columns of a matrix, then its order is

Answer 12

(m x n)

Question 13

A matrix consisting of a single row is called a

Answer 13

Rox Matrix or Row Vector

Question 14

A matrix having single column is called a

Answer 14

Column Matrix or Column Vector

Question 15

A matrix in which each element is ‘0’ is called a

Answer 15

Null or Zero Matrix

Question 16

are generally denoted by the symbol O. This distinguishes zero matrix from the real number 0.

Answer 16

Zero Matrices

Question 17

A matrix A having same numbers of rows and columns is called a

Answer 17

Square Matrix

Question 18

If m = n, then the matrix is said to be a

Answer 18

Square Matrix

Question 19

A square matrix of order n x n, is simply written as

Answer 19

An

Question 20

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.

Answer 20

Principal Diagonal of a Square Matrix

Question 21

A square matrix in which all elements are zero except those in the main or principal diagonal is called a

Answer 21

Diagonal Matrix

Question 22

A diagonal matrix in which all the diagonal elements are same, is called a

Answer 22

Scalar Matrix

Question 23

A scalar matrix in which each diagonal element is 1 (unity) is called a

Answer 23

Identity Matrix or Unit Matrix

Question 24

An identity matrix of order n is denoted by

Answer 24

In

Question 25

[aij]mxn is an identity matrix if and only if

Answer 25

aij = 0 and i ≠ j ; aij = 1 for i = j

Question 26

If a matrix A and identity matrix I are comformable for multiplication, then I has the property that

Answer 26

AI = IA = A

Question 27

They have the same order and each element of matrix A is equal to the corresponding element of matrix B

Answer 27

Equal Matrices

Question 28

is the matrix formed by replacing each element in the matrix Amxn with its additive inverse.

Answer 28

The Negative of a Matrix

Question 29

For every matrix Amxn, the matrix -Amxn has the property that

Answer 29

A + (-A) = (-A) + A = 0

Question 30

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

Answer 30

Multiplication of a Matrix by a Scalar

Question 31

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 .

Answer 31

Addition and Subtraction of Matrices

Question 32

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.

Answer 32

Product of Matrices

Question 33

Multiplication of matrices is not

Answer 33

Commutative

Question 34

A matrix A can be multiplied by itself if and only if it is a

Answer 34

Square Matrix

Question 35

In the product AB, A is said to be _____ of B and B is said to be _____ of A

Answer 35

pre multiple ; post multiple

Question 36

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.

Answer 36

True