Page 76 - DMTH201_Basic Mathematics-1

Unit 3: Matrix

[a ]m × 1 is a column matrix and [a ]1 × n is a row matrix. Notes
ij ij
An m × n matrix is a square matrix if m = n.
A = [a ]m × m is a diagonal matrix if a = 0, when i j.
ij ij
A = [a ]n × n is a scalar matrix if a = 0, when i j, a = k, (k is some constant), when i = j.
ij ij ij
A = [a ]n × n is an identity matrix, if a = 1, when i = j, a = 0, when i j.
ij ij ij
A zero matrix has all its elements as zero.
A = [a ] = [b ] = B if (i) A and B are of same order, (ii) a = b for all possible values of i and j.
ij ij ij ij
3.7 Keywords

Column Matrix: A matrix having only one column.
Matrix: An array of numbers arranged in certain numbers of rows and columns.
Rectangular Matrix: A matrix consisting of m rows and n columns.
Row Matrix: A matrix having only one row.
Square Matrix: If the number of rows of a matrix is equal to its number of columns, the matrix
is said to be a square matrix.

3.8 Self Assessment

Fill in the blanks:
1. A matrix having m rows and n columns is called a matrix of order.................

2. A matrix consisting of m rows and n columns, where m n, is called a.................
3. If the number of rows of a matrix is equal to its number of columns, the matrix is said to
be a .................

4. A matrix having only one row is called a.................
5. A diagonal matrix in which all the diagonal elements are equal to 1 is called.................
Multiple choice Questions:

6. A a m n is a Square Matrix, it
ij
(a) m < n
(b) m > n
(c) m = n
(d) None of these
7. Which of the given values of x and y make the following pair of matrices equal to
3x 7 5 0 y 2
,
y 1 2 3x 8 4

1
(a) x ,y 7
3
(b) Not possible to find

LOVELY PROFESSIONAL UNIVERSITY 69