2.1, 2.2, 2.3 Flashcards Preview

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Flashcards in 2.1, 2.2, 2.3 Deck (21)
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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)=

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

2

in general AB does not equal

BA

3

if AB = AC , then it is not true that

B = C

4

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

0

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 =

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

6

the transpose of a product of matrices equals

the product of their transposes in reverse

7

an n*n matrix A is invertible if there is an n*n matrix C such that CA= I and ....

and AC = I

8

matrix that is not invertible

singular matrix

9

invertible matrix

nonsingular matrix

10

square n by n matrix whose non diagonal entries are zero

diagonal matrix.

11

if ad-bc does not equal 0 then

the matrix is invertible

12

ad-bc equals the

determinant of A

13

det a =

ad-bc

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

x = A^-1b

15

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

the inverse of A-inverse is A

16

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

product of the inverses of A and B in reverse order

17

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

the transpose of A-inverse

18

obtained by performing a single elementary row operation Onan identity matrix

elementary matrix

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

In to A-inverse

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

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

21

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

x