math 2: matrices Flashcards
the size of a matrix is
r by c
r is the
number of rows
c is the
number of columns
the numbers in a matrix are called
entries
entry in the ith row and jth column is named
x subscript ij
two matrices are equal if they are the
same size and their corresponding entries are equal
if r = 1 the matrix is called a
row matrix
if c = 1, the matrix is called a
column matrix
if r = c, the matrix is called a
square matrix
scalar multiplication takes place when each number in a matrix is multiplied by a
constant
if two matrices are the same size, they can be added or subtracted by
adding or subtracting corresponding entries
matrix multiplication takes place when two matrices, A and B, are multiplied to form
a new matrix AB
suppose A is r1 by c1 and B is r2 by c2. If c1 = r2, then AB is defined and has size
r1 by c2
the entry xij of AB is the ith row of A times the
jth column of B
if A and B are square matrices, BA is also defined but not
generally equal to AB
matrix multiplication is not
commutative
the determinant of an n by n square matrix is a
number
the determinant of the 2 by 2 matrix [a/c b/d] is denoted by [a/b c/d] which equals
ad-bc
the product of square n by n matrices is a
square n by n matrix
an identity matrix I is a square matrix consisting of
1’s down the main diagonal and 0’s elsewhere
the product of n by n square matrices I and A is
A
I is a multiplicative identity for
matrix multiplication
a nonsingular square n by n matrix A has a multiplicative inverse, A-1 where A-1A=
AA-1 = I
