Operations with matrices 1. Equality of matrices
Two matrices
of the same dimensions
are considered equal:
А
=
В
, if their appropriating elements are equal, that is
2. The sum and difference of matrices
The
sum
of two matrices
of the same dimensions
is called the matrix
of the same dimension which elements are equal to the sum of appropriating elements of the matrices
A
and
B
.
3. Multiplication of a matrix to number The product of a matrix A on number d (or product of number d on a matrix A ) is called the matrix, which elements are products of a matrix A elements on a number d . Differently,
From the definition of product of number on a matrix its basic properties directly follow:
Let dimensions of matrices
A
and
B
are equal accordingly to
m
×
n
and
n
×
k
, that is the number of columns of a matrix
A
is equal to number of rows of a matrix
B
, then for these two matrices the matrix
C
of dimension
m
×
k
is certain, being their product:
C = АВ
. Elements of a matrix
C
are calculated under the formula:
Calculate determinants of left and right products АВ and ВА .
or it is final:
that is AB ≠ BA .
However, determinants of products
АВ
and
ВА
are equal:

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