INDUMAT Definitions (Quiz 2)

Question 1

Rectangular array of numbers

Answer 1

Matrix

Question 2

Ordered list of n numbers

Answer 2

Vector

Question 3

Matrix where the number of rows equals the number of columns (m = n)

Answer 3

Square Matrix

Question 4

m

Answer 4

Number of Rows

Question 5

n

Answer 5

Number of Columns

Question 6

Square matrix for which every term off the main diagonal is zero

Answer 6

Diagonal Matrix

Question 7

Diagonal matrix for which all elements of the main diagonal are equal

Answer 7

Scalar Matrix

Question 8

Scalar Matrix for which all elements of the main diagonal are 1

Answer 8

Identity Matrix

Question 9

A matrix where elements below the main diagonal are all zeroes

Answer 9

Upper Triangular Matrix (Right Triangular Matrix)

Question 10

A matrix where the elements above the main diagonal are all zeroes

Answer 10

Lower Triangular Matrix (Left Triangular Matrix)

Question 11

Matrix where all elements are zeroes

Answer 11

Null Matrix

Question 12

i

Answer 12

Row

Question 13

j

Answer 13

Column

Question 14

Matrix with only one row

Answer 14

Row Vector

Question 15

Matrix with only one column

Answer 15

Column Vector

Question 16

True or False. A matrix is symmetrical if A = A^T.

Answer 16

True

Question 17

A matrix is considered to be in Reduced Row Echelon Form when:

Answer 17

1. The first non-zero entry in any row is the number 1, called pivots. (So each row can have zero or one pivot).
2. A pivot is the only non-zero entry in its column (so each column can have zero or one pivot)
3. Rows are ordered such that rows of all zeros are at the bottom and the pivots are in column order.

Question 18

Type of matrix that has a determinant value of zero and does not have an inverse.

Answer 18

Singular Matrix

Question 19

Type of matrix that has a determinant value and has an inverse.

Answer 19

Non-Singular Matrix (Standard Matrix)

Question 20

True or False. Identity matrices are nonsingular.

Answer 20

True

Question 21

In iteration methods, if the error is decreasing, then _________.

Answer 21

It is converging towards an answer.

Question 22

If a matrix undergoing an iterative method is not diagonally dominant, then _________.

Answer 22

You must interchange the rows such that the diagonal consists of the highest coefficients of the matrix.

Question 23

In special cases, when no solution exists, we have an _________ System of Equations.

Answer 23

Inconsistent

Question 24

In special cases, we have an _________ System of Equations if an infinite number of solutions exist.

Answer 24

Over-determined

Question 25

A solution obtained when all (n-m) variables are required to 0 (ex. 0 0 16 12)

Answer 25

Basic Solution

Question 26

A solution obtained when at least 1 of the (n-m) variables is not equated to 0 (ex. 1 1 8 6)

Answer 26

Non-Basic Solution

Question 27

A solution where all values of the variables are non-negative (ex. 1 1 8 6)

Answer 27

Feasible Solution

Question 28

A basic solution where all values of the remaining m variables are non-negative

Answer 28

Feasible Basic Solution

Question 29

A solution where at least 1 of the variable assumes a negative value.

Answer 29

Non-feasible Solution

Question 30

A solution where at least 1 of the basic variable has a value of zero.

Answer 30

Degenerate Solution

Question 31

If the determinant of a matrix is equal to zero, then the solution would either be ________ or __________,

Answer 31

No solution or Infinitely many solutions

Question 32

In the Special Cases for iterative methods, m refers to ___________ while n refers to _________.

Answer 32

m = Number of equations n = Number of unknowns

Question 33

In special cases, no solution exists when ___________.

Answer 33

Determinant of the matrix is equal to 0 RDs does not equal to 0

Question 34

Inverse of a 2x2 Matrix Formula

Answer 34

1/ad-bc x [d -b] [-c a] wherein it is the determinant times the adjoint of the matrix

Question 35

In special cases, exactly one solution exists when _________.

Answer 35

Determinant of the matrix is not equal to 0

Question 36

In special cases, infinitely many solutions exist when _________.

Answer 36

Determinant of the matrix is equal to 0 RDs equal to 0

Question 37

Conditions for Convergence for Root Finding

Answer 37

1. |g'(x)| ->1; convergence is slow 2. |g'(x)| < 1; there will be convergence 3. |g'(x)| > 1; no convergence (divergent)