4.4 Matrices: Basic Operations Flashcards
When are to matrices equal?
Two matrices are equal if they have the same size and their correspond-ing elements are equal. For example,
How do we get the sum of two matrices?
The sum of two matrices of the same size is the matrix with elements that are
the sum of the corresponding elements of the two given matrices. Addition is not de-fined for matrices of different sizes.
What is a zero matrix?
What is the negative of a matrix M?
The negative of a matrix M, denoted by
∙M, is a matrix with elements that are the negatives of the elements in M. Thus, if
How do we define subtraction of matrices?
Product of a Number k and a Matrix M
The product of a number k and a matrix M, denoted by kM, is a matrix formed by
multiplying each element of M by k
Product of a Row Matrix and a Column Matrix
Definition: Matrix Product
What is important to remember when it comes to matrix multiplication?
In the arithmetic of real numbers, it does not matter in which order we multiply.
For example, 57=75. In matrix multiplication, however, it does make a
difference. That is, AB does not always equal BA, even if both multiplications are
defined and both products are the same size
