Page 5 - 11-Math-3 Matrices and Determinants

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matrix A. For example,  aaa.a....13.24...1111...............aaaa......1342...2222...............aaaa.....1.342...3333................aaaa...1324. 4444  , in the matrix the entries of the principal diagonal
 
 
 
 
 

are a11, a22, a33, a44 and the entries of the secondary diagonal are a14, a23, a32, a41.
The principal diagonal of a square matrix is also called the leading diagonal or main

diagonal of the matrix.

Diagonal Matrix: Let A = [aij] be a square matrix of order n.

If aij = 0 for all i ≠j and at least one aij ≠0 for i = j, that is, some elements of the

principal diagonal of A may be zero but not all, then the matrix A is called a diagonal matrix.

The matrices

1 0 0 0 0 0 0
2 0 1 0
[7], 0 0 0 and 0 0 2 0 are diagonal matrices.
0 0 0
0 5 0
4

Scalar Matrix: Let A = [aij] be a square matrix of order n.

If aij = 0 for all i ≠j and aij = k (some non-zero scalar) for all i = j, then the matrix A is

called a scalar matrix of order n. For example;

a 0 0 3 0 0 0
a 0 0
7 0  0 0 0  and 0 3 0 0 are scalar matrices of order 2, 3 and 4 respectively.
0 7   0 0 3
,  0 a 
0 0 3

Unit Matrix or Identity Matrix : Let A = [aij] be a square matrix of order n. If aij = 0 for all

i ≠j and aij = 1 for all i = j, then the matrix A is called a unit matrix or identity matrix of order
I
n. We denote such matrix by n and it is of the form:

version: 1.1

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