math 2: matrices

Question 1

the size of a matrix is

Answer 1

r by c

Question 2

r is the

Answer 2

number of rows

Question 3

c is the

Answer 3

number of columns

Question 4

the numbers in a matrix are called

Answer 4

entries

Question 5

entry in the ith row and jth column is named

Answer 5

x subscript ij

Question 6

two matrices are equal if they are the

Answer 6

same size and their corresponding entries are equal

Question 7

if r = 1 the matrix is called a

Answer 7

row matrix

Question 8

if c = 1, the matrix is called a

Answer 8

column matrix

Question 9

if r = c, the matrix is called a

Answer 9

square matrix

Question 10

scalar multiplication takes place when each number in a matrix is multiplied by a

Answer 10

constant

Question 11

if two matrices are the same size, they can be added or subtracted by

Answer 11

adding or subtracting corresponding entries

Question 12

matrix multiplication takes place when two matrices, A and B, are multiplied to form

Answer 12

a new matrix AB

Question 13

suppose A is r1 by c1 and B is r2 by c2. If c1 = r2, then AB is defined and has size

Answer 13

r1 by c2

Question 14

the entry xij of AB is the ith row of A times the

Answer 14

jth column of B

Question 15

if A and B are square matrices, BA is also defined but not

Answer 15

generally equal to AB

Question 16

matrix multiplication is not

Answer 16

commutative

Question 17

the determinant of an n by n square matrix is a

Answer 17

number

Question 18

the determinant of the 2 by 2 matrix [a/c b/d] is denoted by [a/b c/d] which equals

Answer 18

ad-bc

Question 19

the product of square n by n matrices is a

Answer 19

square n by n matrix

Question 20

an identity matrix I is a square matrix consisting of

Answer 20

1’s down the main diagonal and 0’s elsewhere

Question 21

the product of n by n square matrices I and A is

Answer 21

A

Question 22

I is a multiplicative identity for

Answer 22

matrix multiplication

Question 23

a nonsingular square n by n matrix A has a multiplicative inverse, A-1 where A-1A=

Answer 23

AA-1 = I