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qT 200 5, F, 400 5, 200, , 4, , u, , EXERCISE 5-1, , Type I., , 1., , iM., 3ATT, (1), 7 elements is..., having, number, matrices, of, The, i HT., (11) 6 377rai ar 3Ti, IThe number of matrices having 6 elements is 1, , 7 3147, , ., , ., , ..., , 2, () 5 7aa, (1) 13 TTT, , (i)8 37aTa, (V) 18 3Ta, , (ii) 24 s 7 7, , [What are the possible orders a matrix can have if it has}:, i) 5 elements, (11), , 24 elements, , (ii) 8 elements, (iv) 13 elements, , (v) 18 elements

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Mathematics: Class-XIlI, , 5 20, , (ü), A, , is a scalar matrix but not, , diagonal matrix.], , a, , (), JA is a diagonal matrix as well asa scalar matrix.|, 9., IfA is a row matrix as well as a column matrix. then order of A ic, ., , 10., , T, , f, , (Let), , 1, A =[a,]=|3, , 9, , 5, , -6, 15, , 2, , 5, , B lb,=35, , -2, , AM 5ë I, , (and), , 13, 19, , -7, , 12, -5, , ), , 7, , 17, , [order of the matrix A is .], ..., , () a23, (iv) B1 aif.., , (vi), , [order of matrix B is... .], B 444ai A . . [the number of, elements in Bis...], 7 7 (write the elements), bjs' b21, b'33, b24 b23 1 ferd, I, , [NCERT|, , 11., , [Consider the following informations, regarding number, pens possessed, , and, , T, , by Sudha and her two friends, , (Sudha), , (Number of note books), 15, , fVI (Syeeda), , f, , Represent the above, , docs the, , Type Il., 12., , entry, , 09 a, , in the, , Syeeda and Simran], , (Number of pens), , 10, 13, , (Simran), , of note books, , 6, , 2, 5, , informations in the form of a, , second row and, first column, i HAAI, Aufa YTA:, , 3x2 matrix., , represent |, , (then)x=,, y*..., -y7a(hen), x,., , ha, Wid

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A3, 2S, 23 -1T, (and) =|, 0 (and), B=2, +BfT, TT, , 18., , A, , fHata, , -3, , 2, , (in)a b, -b, , 1|-1, , 2, , 4, , a, b a, , a, , cos x sin x, , (11), , (ii), , 2, , 3, , -1, , 5, , sinx, , cosx, , +, , sinx cosx, , cos x sinx, , a b b+c, , 2ab, , 2bc, , a+c2a2+b2-2ac 2ab, , (VI), , 19., , i-2, NCERT, , (v), , (vi), , 3, , find A+B.], tfa i, (Compute the folloWing), 5, 62, , 1, , 0, , (1), , 5, , B, , NCERT|, , NCERT, , -14-612, 7, 6, 8, 5, , 16|+8, , 0, , 28, , 53, , 2, , 5, , INCERT|, , 4, (2, 23, 1, 2 3, 5 -1, 2-3, 5, 0 3 62 0, , afe (IN, , A =4, 5, , 5, , -1.3AfT (find 3A), , 0, , 2, , 20. af (1 A=, faafafan, , -2, , c [-2 -3, , YE (compute thefollowing), , i) A + (B+C) (ii) (A +B)+C (ii) -2A +(B+C) (iv) A +(2B-C), , 45 6, , 2, , 21., 21., , (I) A=-1, , 0, , 2 B=-1 0 1T (and) C =-1, , 1-3-i, , 212, , Af, C) (A B)+C, venf that A + (B- C)= (A - B)- C, A (B, , =, , -1 -2, 2

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Mathematics Class-XII, , 5 24, , 0, , A-4-2, , 2-2, 2, 4, , NCERT|, , 74T (and) B=|, , -5, 29 TE Xan Yfrare aft (Find matrices Xand Y. i) X+ Y =, , (and) X-Y, 30., , 3, , 6, , 9, , [CBSE 1992, NCERT, , o -1, , farr f (Show that) cos6, , cos, , sine, , C o s ot S i n O, , sind, , -cos0, , Cos0, , sin0, , -sin, , INCERT, 31., , f, , (ID 2X +3Y -, , 6I, 32., , ,, , (and) 3X +2Y =, , I[fnd Xand Y.]], , [NCERT, , 2-3, (Given) A =|50, , 3, 27, , (and) B =| 4, , 2, , -1 2, 2 5. 3TE C, , 03, , fhI ai A+C= B(Find the matrix C such that) A +C =B., 33., , af(L) A= 2, zfe, , 47, , 3, , (1)A-3 0 2, , X fr, ft (I), , A=, , -2, , af, , (and) C = - 1 2 7, , 2, , 7 03, , 3-4 5, 0, 6,B=6, , 1, , 2, , -1, , 4, , 3, , -4, , 15, , 2A 3B frETTi (find, 35., , 1, , afs (find the matrix X such that) 2A +3B X+ C., 2, , 34., , 3-4 -51, , 2A-3B.), , 2, 3, 451, A, 0, (I) =|-1, 2. B=-l, , -2-3 1, , 2, , 0, , 3|C=|-1, , 12, , A-2B+3Cfri (find A-2B+3C.), , -1, , 2, 2, , 1, , 3, , -122, , (Also verify that) (A +B) +C= A+(B+ C)i st Frafa i

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Matrices, , 5-25, , 36., , Fatima has two factories at places P and, chocs for boys and girls in three diffcrentQ. Each factory produces sport, price categorics labellcd 1. 2, and 3. The quantities, each, , produced by, , ces given below :], , P, , factory are reprcsented as matri-, , (Facory at P), , Q, , E,frat), , (Boys. Girls), , 95, , 60, , A =75, , 65, , 90, , Factory at Q), , Boys. Girls), , [90 50 1, 2, , B, , 70, , 55, , 2, , 75 75 3 FIT (Find), , 85 3, , [The total production of sport shoes for boys and girls in each, , price category, (i), [The difference ofsport shoes produced by factories atP and Q for, boys and girls in each price category], , Number of sports shoes produced by factory at P for boys and, girls in each price category if production of factory al P (a) re-, , duces to 20% (6) has doubled., ANSWERS, 1., , (i) 2, (i), , (ii) 4, x, , (111) 1 x 24, 24, aV) 1x 13, 13, , 3., , ) A=3, 4, , 4.4x2, 8 3,4 6, 6 4, 1, 2x 12. 12 2, 3 8., 2 9, 9 x2, 3 x6,6 x3, 1, (v) 1 18, 18x 1,, (ii) 1 8,8, , x 5,5x1, x, , x, , 5, , x, , x, , 1.2, , x, , x, , x, , 7, , 6 8, , x, , x, , (i), , x, , x