2.1, 2.2, 2.3

Question 1

let A,B,C be n*n matrices. r and s are scalars
A+B = 
(A+B) + C = 
A + 0 = 
r(A+B) = 
(r+s)A = 
r(sA)=

Answer 1

B+A
A+(B+C)
A
rA+rB
rA+sA
(rs)A

Question 2

in general AB does not equal

Answer 2

BA

Question 3

if AB = AC , then it is not true that

Answer 3

B = C

Question 4

fi the product of AB is the zero matrix, you can not conclude that A =
B =

Answer 4

0

Question 5

let A and B denote matrices whose sizes are not appropriate for the following sums and products 
(A^t) = 
(A+B)^t =
for any scalar r
(rA)^t = 
(AB)^t =

Answer 5

A
A^t +B^t
rA^t
B^tA^t

Question 6

the transpose of a product of matrices equals

Answer 6

the product of their transposes in reverse

Question 7

an nn matrix A is invertible if there is an nn matrix C such that CA= I and ….

Answer 7

and AC = I

Question 8

matrix that is not invertible

Answer 8

singular matrix

Question 9

invertible matrix

Answer 9

nonsingular matrix

Question 10

square n by n matrix whose non diagonal entries are zero

Answer 10

diagonal matrix.

Question 11

if ad-bc does not equal 0 then

Answer 11

the matrix is invertible

Question 12

ad-bc equals the

Answer 12

determinant of A

Question 13

det a =

Answer 13

ad-bc

Question 14

if A is an invertible n by n matrix, then for each b in R^n, the equation Ax = b has the unique solution

Answer 14

x = A^-1b

Question 15

if A is an invertible matrix, then Ainverse is invertible and

Answer 15

the inverse of A-inverse is A

Question 16

if A and B are n by n invertible matrices, then so is AB and the inverse of AB is the

Answer 16

product of the inverses of A and B in reverse order

Question 17

if A is an invertible matrix, then so is A^t, and the inverse of A^t is

Answer 17

the transpose of A-inverse

Question 18

obtained by performing a single elementary row operation Onan identity matrix

Answer 18

elementary matrix

Question 19

an n by n matrix A is invertible if and only if A is row equivalent to In. any sequence of elementary operations that reduces A to In also transforms

Answer 19

In to A-inverse

Question 20

A is an n by n matrix. the following statements are equivalent. All are truee or all are false
A is an 
A is row equivalent to the 
A has _ pivot positions 
the equation Ax= 0 has only the 
the columns of A form a 
the linear transformation x to Ax is 
the equation Ax = b has 
the columns of A span 
the linear transformation x to Ax maps 
there is an n by n matrix C such that 
there is an n by n matrix D such that
A^t is an \_\_\_\_ matrix

Answer 20

invertible matrix
n by n identity matrix
n pivot positions
only the trivial solutions
form a linearly independent set
is one to one
at least one solution for each b in R^n
R^n
maps R^n onto R^n
CA = I
AD = I
invertible matrix

Question 21

x(A) = Ax so Ax(A-inverse) =

Answer 21

x