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What is matrix?

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A rectangular array of mn numbers (real or complex) in the form of m horizontal lines (called rows) and n vertical lines (called columns), is called an mxn matrix (to be read as m by n matrix) or matrix of

order mx 12 211 012 ain a 21 2212 A mx 17 matrix is usually written as, A = = a 22 : : : : a mi a m2 a mn mxn ij A matrix may be represented by the symbols [a; ], (a;j) or by a capital letter A, i.e. A = [a;; ]mx n or (a;;)mxn The numbers a11, 212,... etc. are known as elements of the matrix A, a;; belongs to the ith row and ſth column and is called the (i, j)th element of matrix A = [a;j ] > = Note A matrix is not a number and it has no numerical value. ])-2

EXAMPLE 1. Construct a 2 x 2 matrix A=(a;), whose general element is given by a, = (i + 2 T9 257 [9/2 25/27 (9 57 [9/2 257 b. d.

8 9 4 18

9

4

8

18

- = Sol. b. 241 = (1 + 2)/2 =9/2, 212 = (1 + 4)2 / 2 = 25/2, 221 = (2 + 2)2 / 2 = 8, 2,2 = (2 + 4)2 / 2 =18 212] [9/2 25/27 a21 (ау 1 = A= 8 18 222

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