## Std 12, Commerce, Maths And Stats Part-I

Welcome back, Dear Students In this Module we will be understanding the definition of matrix And Order Of a matrix. Starting with a first part definition of matrix understand dear students, a matrix is a ordered Rectangular array, array ka matlab arrangement, arrangement kis chiz ka, Arrangement of numbers. Example 1 2 3 4 5 6 Or arrangement of functions cosA -sinA tanA. So matrix is an ordered rectangular array of a numbers or functions enclosed in brackets. Agar aapne yaad rakha hai brackets apan ne padh liya hai pehle wale module me, there are two type of brackets we can use that is nothing but rectangular bracket or the round bracket so ye hota hai matrix ka notation, ek matrix ka presentation. Moving further matrices are usually donated by capital letters understand dear students jab matrix ek se zada sath me aate hai to usko bolte hai matrices matlab matrix is singular and matrices are plural. So it is always denoted by capital letters A, B, C, and so on and jo ander ke values likhe hai apan ne jo ander ke numbers ya functions likhe hue hai usko bolte hai elements of that matrix. Elements of matrix hamesha small letters se represent hota hai. In a matrix the horizontal line of elements usko apan bolte hai Rows of that matrix and it is usually denoted as R1, R2, R3….. Similarly jo vertical lines hai usko kya bolenge, vertical lines are nothing but columns. And it is represented by C1,C2, C3 and so on moving further ye hua definition. Definition ko aur ek bar revise karenge , A matrix is an ordered rectangular array of a numbers or functions enclosed in brackets either a rectangular bracket or the round bracket ab ye pure definition me Important part hai ordered word ka . What Is order of matrix,order ke liye we will understanding the next part. Here we have, the order of a matrix, suppose we have a order of matrix which we have to understand uske liye meko ek matrix chahiye pahile , so the order of matrix having m rows . mere pass m rows hai and N columns hai uska order ky hojayenga order will be m*n that is nothing but we can say as a matrix of order m*n. ab m*n ko mein ek aur tarikhe se read kar sakta hu that is m/ n that means I can say that the given matrix A is having the order as m by n where m stands for no. of rows to yahape mere pass rows kitni hogi m rows hogi. N represent numbers of columns , matlab columns kitni hogi n columns hogi. So the order of this matrix will be m/n, m/n matlab number of rows is m and number of columns is n. the element of matrix A, suppose for a example agar aap first row and first column ka intersection dekhkhoge to konsa element milega aapko , aapko milega a element named as a11. Ab ye a11 ka matlab ky hai , jo nichewala suffix mein phehla one hai that represents the row, and the 2nd number jo dusra diya hua hai 1 suffix ke ander that represents the column matlab main aapko agar bolu a21 , a21 ka matlab second row and 1st column. So in general, if I want to say that the element which belongs to the ith row and jth column of matrix A will be denoted by aij. Matlab mai pura matrix main compact way mein likh sakta hoon as matrix A=

[aIJ] of the order m/n . Understand I or j ka value Suffix me aayega. Where I represent what 1,2,3,4,……mth row tak and j represent 1 ,2,3,4,…..nth column tak. Moving further , As matrix ‘A’ has,’m’ rows and ‘n’ column and if I ask you no. of elements kitne hoge uske ander then the rules say that the number of elements will be ‘m*n’ that is mn. Example dekho yaha pe, suppose ek matrix hai mere pass jiska order hai do rows ka aur teen columns ka. Matlab order ky hogaya 2/3. So the number of In this matrix will be 2*3 which is equal to 6 .that means muje yahan pe 6 elements mujhe andar dikhenge. So always remember no. of elements agar aapko dhundna hai kitne no. of elements hai always multiply number of rows with number of columns. So moving further we have the Difference between Determinant and matrix , if you remember determinant you have studied in the lower standard and matrix your are learning now so what is difference between determinant and matrix ka bich ka difference first point , A determinant is expressed, with the help of vertical bars , but where as a matix is expressed with rectangular brackets , ye first difference hai, second difference in determinant the number of rows will be equal to numbers of columns, matlab for example agar aap neche dekhoge A aur B determinant dono mein rows ka value aur columns ka value equal hai 2/2, 3/3 but this not the case with matrix, matrix mein aisa koi restriction nhi hai for example if you check matrix B no. of rows is 2 no. of columns is three dono equal nhi hai phir bhi chalega and then we have the third point Determinant is reduced to a value, agar aap dekhoge A ko solve kerne pe zero milega, B ko solve kerne se 54 milega where as matrix has no such value isko aap khali ek arrangement of numbers ke format mein likh sakte ho.