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
