CHAPTER 2: Matrices Flashcards
A set of mn numbers (real or complex), arranged in a rectangular formation (array or table) having m rows and n columns and enclosed by a square bracket [ ]
Matrix
A matrix consisting of a single row
Row Matrix/Row Vector
a matrix having single column
Column Matrix / Column Vector
A matrix in which each element is ‘0’
Null or Zero Matrix
Zero matrices are generally denoted
by the symbol ____
O
A matrix A having same numbers of rows and columns
Square Matrix
A matrix A of order m x n can be written as ______
Amxn.
If m = n, then the matrix is said to be a ______
square matrix.
A square matrix of order n x n, is simply written as _____
An.
The ______ of a square matrix is the ordered set of elements aij, where i = j, extending
from the upper left-hand corner to the lower right-hand corner of the matrix.
principal diagonal
A square matrix in which all elements are zero except
those in the main or principal diagonal
Diagonal Matrix
In diagonal matrix, some elements of the principal
diagonal may be ________
zero but not all.
A diagonal matrix in which all the diagonal elements are same
Scalar Matrix
A scalar matrix in which each diagonal element is
1(unity)
Identity Matrix or Unit Matrix
An identity matrix of order n is denoted by _____.
In
If a matrix A and identity matrix I are comformable for multiplication, then I has the property ______
AI=IA=A
Two matrices A and B are said to be equal if and only if they have the ______ and each element of matrix A is equal to the corresponding element of matrix B
same order
The negative of the matrix Amxn, denoted by _____, is the matrix formed by replacing each element in the matrix Amxn with its ________
–Amxn; additive inverse.
If A is a matrix and k is a _______, then ____ is a matrix whose elements are the elements of A, each multiplied by k
scalar (constant); kA
If A and B are two matrices of _______ m n then their sum A + B is defined as C, m n matrix such that each element of C is the sum of the corresponding elements of A and B.
same order
Two matrices A and B are said to be _____ for the product AB if the number of columns of A is
equal to the number of rows of B.
conformable
Multiplication of matrices is not _____
commutative
A matrix A can be multiplied by itself if and only if it is a _______
square matrix
