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EXERCISE, , 2, , 1., , 3, , 3, , 3, , 1 and B1, , 2, , ()7 2 3, , 7, , (132 7, If A, , 2., , 2, 2, , 2, , then 3 B - 2 A =, , 3, , 3, , (3), , 2-3 2 7, , B382 and 2X +A = B then X, 7, , 6, A=6, , (1), , 4., , 2, , 3 1, , 1, , 2 -1n, , -1, =0 -1 5,B, 5, , 3 50, , 23, , If A= |1 2,, 5 6, , =, , |5, , 6, , (3)3-5, , 0, , 6 -1 8, , and Á +B-C, , 2 1, , (A)21, , 3 and A +B-X= O then X =, , 6-3 8, B, , 1 3, , (3)2-1, , 0, , 6-2 8, , -23, 4)-3 2, , =, , 3, , (1), , 3 If, , [7 23, 3 2 7J, , =, , O then C, , (4), , none, , of, , these, , =, , 5 5, , (1)6, , (2-4, , 77, , 5., , If A+B, , 3 5, , 23 1, 6, , -1 5 and, , 22.0, , (1)|3 04, 6., , (4) none of these, , 77, , A-B- 21-1, 0 -13 then, B=, then B, , (230 1, , 10, , o, , 1-1, , (3)-30 1, , (4) none of these, , IfA+ B=|1 and A-2B =|0 -then A=, 11, , (2) 22, 7., , (3) 0 6, , x+3 2x7 8, , If6, , (1) x = 0 , y =0, , 3, , o, , then, , (2)x = 3, y = 4, , (3), (Chapter-1), , x=, , 4, y, , =3, , (4)x=-4, y =-3, , Radiant'S

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1.17, , Matrices, 8, , x-3 2y -8, , If z+2, , 2 a 4 4 then x y t, (4)2, , ()0, , 99., , (2)1, , X+3, , 2y +x, , 1fx-1 4a-6, ()0, , If A, , 15, , 8, , -1 10, , 9, , -2, , 2, , 10, , 15, , 8, , 7, , ., , then additive inverse of A, , (2) 1 5, , -11., , (4), , 1 0, , i, , 2, , 9, , -10, , -15, , -8, , -10, , 9, , *", -2 10, , o 1, -i, , If A =|0, , 2, then additive inverse of A, , -15, , is, , i01|, , i 0 17, , (2), , 1)0-, , -1 15, [i, , 0, , I -I-5, 0, , (4) 0 1 0, 0, , 2 5, , 1 2 . I fA =, , 1 12, , 2, (1) AB=0,, , -2, , i, , 0, , 0, , -1, , (3)0-i 1|, I, , 10, , 8, , 0, , (3) 0, , is, , 7-1, , (1)-1 10 9, -2 2 -10, , 0, , 4)3, , (3)2, , (2)1, 7, , 10., , then x y a, , 4 2a, , BA=0, , 0 1, , then, , (2) AB, , =, , 0, BA, , #, , (3) AB, , 0, BA =0 (4) AB, , *, , 0, BA, , #, , 0, , 3, , 13IfA, , 0 0, =0 3 0| then A2 =, , (1) 31, , 14. IfA=, (1) I, , o, , 0 3, , (2)3A, , (3) 91, , (4) 9A, , (3) 0, , (4), , 01 thenA =, (2)-1, Radiant's, , none, , of these, (Chapter-1)

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1.18, , 2 11 B15. IfA= 3and, 7, , 4 4, , (1, , 3, 16., , 2 0 then AB =, , (2), , 212, 0, , If A=|-1, , 0, , (24 612, 2 3 4, 2, , 1|,B =|1, , 0, , 2 - 1 12, , 5 9-13, 4, , 3, , 5, , (3)7 4 4], , 9 13, , 2, , o, 1-2, IfA =|-1 0 and B = |1, , 3)2, , (4) does, , 12, , not, , exist, , then AB =, , (2)-124, , -22 4, , 17., , 2 47, , 2, , (1)1 2, , Algebra, , 5 9 13, , 5-9 13, 3)-1 2 4, , 4)-12 4, , -2 2 4, , 2 4, , -2 2 4, , 1 2, 2 3 then AB =, , 2 34, , 2 -1, , 3 21, , (1) 5, , [3-25, , (3) 5-5, , -7 8, , 7-8, , (2) 5, , 8, , (4) not defined, , 12 2, 18., , If A= |2, , 1, , 2| then A2- 4A-61 =, , 2 21, (1) 0, , (2)I, 1, , 19., , If A = |2, , 2, , lfA|1, , 1 2| then (A + I) (A- 51) =, , 2 1, , 4, , and A, , (1) 1, , 21., , (2) Unit matrix, , 1 21, , then A, , (3) Scalar matrix, , - kA- 41, = 0 then k, , (2) 2, , fA-0, , (4) none of these, , 2 2, , (1) Null matrix, 20., , (3)21, , =, , (3)-2, , (4) -1, , =, , 2 n, (Chapter-1)=, , (4) Diagonal matrix, , (4), , Radiant's, , 12n, , lo

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.1.19, Matrices, , 2. IfA=3 4], 22., , 1IfA=1 -1, , thenA", , (1, 23., , (2n, , -n, , -=, , IFA, IfA, , 3, , 2+n 5-n|, , [ 3n -4n, , (-4, , (4), , ) | r -D°J, , none, , of these, , [4 2, , then (A - 21) (A -31)=, , (4) 51, , (3) 0, , (2)I, , (1) A, , 23, , 1-2 31 and, , I f A-4, , 4, , B=, , 5, , then, , 2 1, , are equal, (1) AB, BA exi_t and, are not equal, (2) AB, BA exist and, exist, , BA does not, , (3) AB exists and, exist and BA exist, (4) AB does not, , a2, , -b, , 0, 25., , If A, , =, , 0, , -c, , and, , a, , (4) O, (3) I, , (2) B, , cos sin, IfA=- sin 6 cos, , then A, , =, , cos 59-sin 50|, , sin56, , cos 50, , (2 sin5e cos58, , ()-sin50 cos50, sin507, , COs S6, , then AB, , ac be c, , (1) A, , 26., , ac, , B- ab bbe, , -a 0, , b, , ab, , (4) none of these, , (3sin 50 -cos560j, 4, , 27., , If A=|- kand A*, , andI0.1, , IfA=, , (2) I, , (1) O, , i, 29., , IfA|0, (1) I, , O then k, , =, , (4)-2, , (3) 2, , (2)-1, , (1) 1, 28., , =, , then A* (a + d) A- (bc ad) I, -, , =, , -, , (3) 21, , (4) a- d, , 0, , then A" =, (2) A, , Radiant's, , (3)-A, , (4), , none, , of these, , =(Chapter-1)

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1.20, , 30. If A=|-2, , then A, , a, If A = | ab, , b*, , ac, , bc, , 33., , IfA=, , (3) SA, , (4) 5 A, , ab ac, be, , and a +b+c = I then A, , c, (3) A, , (2) A, , (1)I, 32., , =, , (2) nA, , (1)A, 31., , Algetr, , (4) A3, , [N.y};B=|h b:C=thenABC, , (1) (ax + hy + bxy), , (2) (ax+ 2hxy +by, , (3) (ax*- 2hxy + by-), , (4) (bx - 2hxy + ay, , IfA=0 1then AA =, I, , (4)2 5, , (2, 1, 34., , I fA =, , 2, , 2 2, , 21-2 then AAT =F, -2 2-1, , (1) I, , (2) 31, , -4, , 0, , 0, , (4)-9I, , 40 0, , 65) IfA=040, |0, , (3) 91, , and B= |0, , 04|, , 4, , 0| then (AB), , =, , 0 04, , (1) 16 I, , G6, , (2) 641, (3) 2561, (4) none of these, If A is symmetric matrix or skew-symmetric matrix, then A is, , (2) Skew-symmetric, , (1) Symmetric, (3) Diagonal, , (4) Scalar, , -12 3, If A = 2, , 3, , 3, (1) 3, , 6|, , is, , a, , symmetric matrix, then, , x, , =, , x 7, (2) 6, , (3) -6, , (4) 0, , o, 2 1, (38) If A =|-2 0 -2 is skew-symmetric matrix, then x =, , -1x0J, (1) 0, (Chapter-1), , (2) 1, , (3) 2, , (4)-2, Radiant's

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1.21, Matrices, , 0 42, 9, , IfA, , 0, , 4, , =, , 8, , is a skew-symmetric, then, , x, , 2-8, (2) 1, , (1) 0, , A-, , A, , (4), , is, , =, , skew-symmetric, , a, , matrix, then (x,, , [o, , y), 4, , (3) (5,, , (2) (-1. 1), , ()(1. 1), , 4, , (3) 2, , 10. 0), , 5), , 4, , .IfA =|-10 7 then Ais, 4, , 7, , of, , 0, , (4), , (3) idempotent, , (1) symmetric (?) skew-symmetric, 4-x, , 5, , is a, , 42 If A|2x +10, sin, , cos, , 43., , Ioa, IfA1, 0n d, , If A, B and AB, , are, , (2), , (1) A=B, , (4) A, (3) A, , A is the, , then, identity matrix,, , If A=|, , 0, , symmetric, AB, , =, , -1/2, , (3) AB II, , Trace, , of A =, , 2, , (4), , 1, , 3, , IfA =|3 1B3 4, , (1)5, , is, , (2) 10, , Radiant's, , (4) 4, , (3) 2, , (2) 1, , 2 1, , 48., , of these, , -5, , -1 5, of A |2, 2 0 1, =, , (1)0, , none, , (2) 1, , (1) 0, , 47., , (4) 2, (4) AB B A, , matrices then, , (3) 2, , trace, , =, , 0, , 2then, , -1, , x, , (3)1, , 2 1/2, , The, , (4)-5, , (3) 5, , (2)-1, , (1) 0, , 46., , =, , (2)1, , x, , 45., , x, , then AA=, , IfA-sin0 cos, (1)0, , 44., , then, symmetric matrix,, , (2)-2, , (1)2, , these, , none, , then Trace, , (AB), , =, , (4) 45, , (3) 15, ********, , ewwwww.www, , wwwssteertvose, , (Chapter-1)

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Alge, , A.22, 1 2 -1, , then T, (3A), , 2 4, , 49 IfA=|3, , =, , 71 2, , IfAis, , $0.), , skew-symmetric, , a, , 1, 53., , =, , none, , of these, , (4) 13, , =, , (4) 2A, , (3) A, , (2) I, , (1)0, , (4), , 3) 10, , -0, IfA=lo 2 then A* -A?, , 52., , T, (A), , 3m + 7n=, , [10 -11], , =, , (2) 5, , (1)3, , xn, then, , (3) n, , m[-3 4] +n [4 -3], , 51., , of order n, , matrix, , (2) 0, , (1)1, , (4) 45, , (3) 15, , (2) 10, , (1)5, , 2 2, , If A =|2 1 2 then A$-442-6A=, , 2 2 1, (2) A, , (1)0, 54., , IfA3, , (1)-6, 4,, , (5., , 4, , kA=0 3a, , kA=h 24 hen the values of k, a, b are respectively., , 2b 24, , (2) -6, 4,, , 9, , (3) -6, 12,, , -9, , A square matrix [a] in which a,, , (1), , (4) I, , 3) -A, , Unit matrix (2), , Scalar matrix, , (4) -6, -12, -18, , 18, , 0 for i * j and a, =k (a constant) for i =j is calleda, (4) Diagonal matrix, , (3) Null matrix, , cosa sin a, 56., , 57., , =, , (1) A (a) - A (B), , (2) A (a) + A (B), , (3) A (a-B), , (4) A (a +B), , The, , order of the matrix A is 3, , (1)2x3, 58., , then A(a). A(B), , If A(a)=-sin a cosaj, , 5 and that of B is 2, , x, , 3. The order of the matrix BA 1, , x, , (4) 5 x2, , (3) 2 x5, , (2) 3 x 2, , If (1 2 3) B = (3 4) then order of the matrix B is, , ()1x3, , (4) 3 x 2, , (3) 3x1, , (2) 2 x 3, , ah, 59., , The order of [x y, , z] |h, , f, , b, , Y, , is, , Lg f c, , (1) 1x 3, 60., , The order of the, (1) 2 x 3, , IChapter-1)-, , (3) 3 x3, , (2)3x1, matrix A, (2) 3 x 2, , is, , 3, , x, , 5 and that of B is 2, , (3) 2x5, , (4) 1x 1, x, , 3. The order of the matrix, , (4) 5 x 2, , -(Radiant's, , BA

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=, , 1.23, , Matrices=, , 10-2, 61., , lf A |3, , -1, , =, , 4, , 5 6, , 2-1 4, If A=| 0, , 5, , -2, , (4) 19, , (3) -16, , (2)-8, , (1)8, 62., , then the cofactor of 5 is, , ,, , 2, , , then the minor of-1 is, , -3I 3, (1) 15, , (4) 4, , (3) 4, , (2)-15, , -10 5, , 63., , IfA, , 2-2|, then the cofactor of -5, 45 3, , =, , (4) 9, , (3) 6, , (2)-3, , (1) 3, , 64., , ., , is, , then the minor of a,,is, 44,, 3, =|2, , If A, , 3242, (2) 51, , (1) 41, f, , a, , (4)-56, , elements,, matrix has 7, x, 1 x 7 or 7 I, , (1), (3) 2, , (3)43, , 7, , x, , or, , 1, , 7, , orders of thè, , then the possible, 1 x 14, , (2), , or, , 14, , x, , matrix are, , 1, , (4) 7x 7, , 2, , x, , -1 2, , then det A, 0 4,, 66 If A= 3, 4 2 5, , =, , (3) -11, , (2) 39, , (1) 27, , [i0 1, 67, , IfA, , =, , |2, , 1, , 68., , 0, then, det A, , =, , 3 2 1, then the determinant, , IfA 2, , A?-2A is, , (3)-5, , (2) 25, , (1)5, , (4) 5, , (3) 4, , (2) 3, , (1) 2, , (4)-35, , (4)-25, , I0 0, , 69, , IfA2, , 3, , 4, , and, , det A =45 then x, , ==, , 5 -6 x, (1) 23, , (2) 21, , Radiant's, , (3) 13, , (4) 7, , =(Chapter-1)

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1.24, , Algebr, , xIy+z, 70, , y, , 2+x, , z, , x+y, , (1) 1+x +y+z, , (2) x+y+z, , (3) 0, , (4) I, , (2) 1993, , (3) 1994, , (4) 0, , 1990 1991 1992, 71., , 1991, , 1992, , 1993, , 1992 1993 1994, (1) 1992, , loge loge loge, , 72 loge loge loge, , ECET 2017 (AP, , log e loge loge, (1)0, , (2) 1, , (3) 4 log e, , (4) 5 log e, , (3)-2, , 4) 2, , 1 x 2x, 73., , Ifx, , #, , 0 and, , |1 3x 5x=0 then x ==, 1 3 4, , (1)1, , (2)-1, , 1, , 74., , If 1,, , o, o, , are, , the complex cube roots of unity, theen, , 1, 1, , (1)0, a, , (2) 1, , (3)2, , (4) 3, , b c, , bc a, , Ca b, (1) a +b + c, , (2) a+b' +c-3 abe, , (3) 3abc- a? - b'- ce, , 76., , 12 x, , If|4 -17, 2 4-6|, , is, , a, , singular matrix, then x =, , (1)0, 77., , (4) 0, , (2) 1, , (3)-3, , (4) 3, , 8-6 2, , If the matrix A =-6, , 74, , |2-4, ()3, , (2) 4, , is, , singular,, , then, , (3) 2, , =, , (4) 5, , (Chapter-1):, , Radiant's, , =

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1.25, MatriceS, , 2-14, If X01|, , 78., , 1, , is, , a, , singular matrix, then x =, , 2 0, , (4) 5/8, , cos, If the matrix, , 79., , (3) 3/8, , (2) -1, , (1) 1, , sin 0, , sin, , 0, , cos6, , 0, , 9=, is singular, then, , 0, (4), , (2), , (1) T, 80., , of a, lf each element, , ne, , prOduct, , square, , (3), , of two, , non-zero, , square, , multiplied, , matrices A, , then, , (2), non-singular, , (1) A, B are, non-singular,, (3) A is, , of the, , determina, doubled, the, multiplied, matrix is, , (2) doubled, , (1) not changed, 81., , nant, , of a, , row, , 15, matriX, , 3), , but B is singular, , and B, , atleast, , by 1/2, , of the, ofA, , (4), , m a t r i x ,, , z e r o, , ne, e, sam, , o, dc, eir, or, rd, , is, and B, , one, , singular, (4) A is, , by 4, , is, , a, , singular, , n o n - s i n g u l a r ., , is, but B, , 1 a b +c, 82., , 1b c, 1, , (4) (a, , c a +b}, , (2) a, , (1) abc, , +b +, , c), , +b +c, , 1, , 83., , 1, , 1+X, , 1, , (4)-xy, , 1+y, , (3) xy, , (2) y, (1) x, , 84., , Ifo, , is, , one, , of the complex, , cube roots, , of unity, then, , 1, , w, , o, , 1, (4) (1 - w), , (3)-3, , (2) 3, (1) 0, , a+b, 85., , a, , b, , a, , a+C, b+C, , (2) a, , (1) abe, , Radiant's, , b2ca2, , (3) 4a, , b, , c*, , (4) 4abc, ww..wxANNNAWRAU, (Chapter-1)

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1.26, , Alge, y+Z, , 86., , z, , Z, , Z+X, , X, , X, , X+Y, , y, , (2) 2xyz, , (1) xyz, 1, 87., , The value, , 88., , (3)-7-4i, , (4) none of these, , 1=, , of | 1 + i i, , 1+i, , 1, , (2)-7+4i, , (1) 7+ 4i, , e, , (4) 4xyz, , 1+i i, , i, , If 0, , (3) 3xyz, , R, maximum, , |1, (2), , (, , is, , 1 1+sin0, , value of, , 1, , 1+cos, , 32, , (3) 2, , (4), , (3) 4!, , (4) 5!, , (3)-1, , (4), , 4, , 1! 2! 3!, 89., , The value of | 2!, , 3!, , 4!, , 3! 4! 5!, (2) 3!, , (1) 2!, a-b, , 90., , b-c c-a, , b-c. c-a a-b=, , C-a ab b-c, (2) 1, , (1) 0, , 91:, , a-b-c, , 2a, , 2a, , 2b, , b-c-a, , 2b, , 2c, , 2c, , 92, , +, , a-b-c, , 2b, , 2c, , 2a, , b-c-a, 2b, , 2c, , 2a, , (1) a +b, , (Chapter-1), , +c, , of these, , c-a-b, (2)a, , (1)0, , none, , b +c, , (3) (a + b + c, , (4) (a +b+cP, , C-a-b, , (2) (a + b + c, , (3) (a + b + c), , (4) (a + b + c, , Radiant's

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1.27, , Matrices, 93. If a, b,, , distinct and, , c are, , bbb-1| =0then, ( 4 )a b c= I, , (1) atb+c=1, 94., , x +a, , b, , a, , X+b, , a, , b, , If, , +, , +, c) (3)0, -(a, , =, , If, , b+c+2a, , k, , (a, , +, , b, , +, , (4), , b+, , c), , c)2, , then k, , c+a+2bb|, , a, , =, , (4) 2 (a, , +b, , +c), , (3)-2, , (2) 2, , The solutions of the equation, x+1, , 2, , 3, , 1, , X+2, , 3, , 1, , 0, , are, , 2 x+3, , (4) 0, -6, , (3) 0, 6, , (2)-6, , (1) 0, , X-a, Xa X-b|, , 0, A root of the equation, , X+a, X+b, , 0, , -c, , 00 isis, , =, , X+C, , ( 4 ) ( a +b + c), , (3)-, , (2) 1, , (1) 0, , the equation, A root of, 3x-8, , 3, , 3, 3, , = 0 is, , 3x-8, , 3, , 3, , 3x-8, , 8, (3) 3, , 2, , (1), a-x, 99., , +b, , a, , b, , a, , (1) 1, , 98., , (3), , = 0 then x =, , (2) 0, (a +b, , C, , 97., , 0, , X+C, , a+b+ 2c, , 96., 96., , ca, , +c =0, , C, , (1) a +b +c, , 95., , (2) ab + bc +, , =, , Ifa, , +b+c, , (1) x = 0, , =, , 0,, , one root, , of, , C, , cb-x, , (4)3, b, a, , = 0 is, , b a c-x, (2)x=1, , Radiant's, , (3) x 2, , (4), , x, , =, , a +b2, , +, , c?, , (Chapter-1)

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1.28, |7 6, , x, , 100. If one of the roots of 2, , x 2, , x, , 3 7, , (1)2,6, , 0 is, , (2)2, 7, , b+c, 101. If, , Ala, , ab, , cb, , ca, , (1)1, , roots are, , (3) 3, 6, , (4) 3,7, , ac, , c+a, , ab, , 9, then the other, , ka' b, , be, , c* then k =, , a+b, , (2) 2, , (3) 3, , (4) 4, , 102. The matrix 21 0 is, , 31, (1) singular, , (2) non-singular, , (3) symmetric, , 103. If A is 3 x 3 matrix and det (3A) =k det A then k, (1)9, (2) 6, (3) 1, , 104. The adjoint, , (4) 27, , 2-3, , of the matrix4, , 6, , -6 3123-r, , (4, , (2)4 2, , 105. The adjoint of the matrix, , (1, (3), , cos, sin a, COs a, , -Sin a, , coso, , -6, , 4)4, , (3), na, , Sin a, , COS a, , -Sin a, , (2), , cos, , Cosa, , sina, , -Sin a, , cosa, , -cosa sin a, , Sin, , (4)-sina, , cOsa, , -coS aj, , [I2 11, 106. The adjoint of the matrix, , 3, , IS, , 12, [-3 11, , (1)-31, 4, , -, , 3 1, , (2) 3, , 1, , 40 4, , -2 1, , (3)21 -1|, 4 0 4, .wwntm, , (4) skew-sym, , (4) none of these

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1.29, , Matrices, , 107., , 2e 2, , i Jo 2, , IfA =|-11-2, , and, , o, , x, , adj. A =, , 0 ,then, toot 2, , = 4, y =- 1, , (3) x = -4, y = -, , 108. IfA=, , 3 4, 5 6, , 4. y = 1, , (2)x, 1, , A4)x, , 4, y, , =, , =, , 2, , 1, , then Adj (Adj. A) =, , (1) A, , (4) -2A, , (3) 2A, , (2)-A, , 109. IfA=|2 3 then adj (adj.A) =, 4 6, , 110., , 111., , 12., , If Ais a, (1)2, , 3, , x, , 3 matrix and if JA|, , =, , 4, then ladj.A|, , (2) 4, , (3) 8, , (1) 0, , (2) 1, , (3)-1, , Let A and B be two, , symmetric, , If AA' =I then |A|, , (4)-2A, , (3)-A, , (2) 2A, , (1) A, , =, , (4) 16, , =, , (4) +1, matrix AB, order. Then the, , same, matrices, (2) Skew-Symmetric matrix, , of, , (1) Symmetric matrix, (4) Identity matrix, , (3) Null matrix, , x1 11, 113., , If2, , 3, , 4, , has, , no, , inverse, then the real value, , is, , (4), , (3) 0, , (2) 3, , (1) 2, , of x, , -1 x, 114., , If1, , x, , 1, , has, , no, , inverse, then the real value of x is, , x-1 1, (2) 3, , (1) 2, , 2, 115. If the inverse o f 4 -, , (3) 0, , (4) 1, , x, 7, , does not exist, then x =, , 2 4-6, (1)0, , (2)1, , Radiant's, , (3) 2, , (4)-3, , -, , BA 1S

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1.30, 116., , inverse, , The, , 21, , of the matrix l3-sSs, , (1), (4)none of these, 117. The, , multiplicative, sin, , sin, , inverse, , cos, , sin 0, o|-cos6, -cos sin, , cos, , -sin6 cose, , (1-cos sin6, , (2) cose -sin, , 3Sin8-cos0), , cos, 118., , (4) sin, (4), , sin0, , IfA =, , a, , 3, , 2, , b 0 then A- =, , 0, , 0 c, , (1) A, , 1/c, , (2) I, , 0, , 7-3-3, , 11 1, , (1)3 4 3, , 0 01, , 0, , 1, , o, , 0, , 0 1/a, , 1/a 00, (4) | 0 1/b, 0, , 0, 1/¢, , 100is, , -10, , 131, , (2) 4 3 8, , (3) 3 3 4|, 3 4 3, , multiplicative inverse of the matrix A, 0, , 0, , (30 1/b o, , 120. The inverse the, of matrix -1, , [0 1-1, , (2), , 1 0, , -10 0, (Chapter-1)=, , cos6 sin 6, , 2, , 0 0, , 119. If A =0, , (1), , cos, , then 8A-=, , 3, , 121. The, , 1S, , =, , |0, , 1 0, , 41 4 3, , is, , -1001, (4)0 1 0

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1.31, , Matrices, , 1 23, 122., , 3 4, , If A =|2, , then A, , =, , 3 4 6, , 123, , 2 0(1)03 2, -2(123., , The, , o, , (2) 2, , 34, , 3, , 4 6, , is, , known, , 3, , 0, , (3), , -2, , (4), , none, , of, , I-2, , 5, , matrix-5, 7, , -20 2, , 0, , 11, , -11, , 0, , as, , (2) diagonal matrix, ( 4 )s k e w - s y m m e t r i c m a t r i x ., , (1) symmetric matrix, , matrix, (3) upper triangular, , 24., , lf A, , is, , a square, , matrix such that A, , are, , square, , any 2, , x, , 2, , matrix, , matrices, , 0, , 0 4, , of order 3 such, , then det, , (Adj., , A), , 27. A4, , JA, , (3) 20, , |B|, , =, , 3 then |3AB|, , (4) 81., , (4), , 100, , then A=, , 2, , o-1, , then A-l ==, , -30 16, , -1 -30 16, 3, , 3, , -1,, , 0, , 128. IfAo 1, , 30 -16, , =, , 10 01 then |A|=, A,if A(adj.A) =a, , o, , ay1, , that, , (3)-81, , (2) 10, , (1) 0, , 2, , 4, , (3) 64, , (2)-27, , (1)-9, , 126., , 0, , {0, , (2) 16, , IfA and B, , For, , (Adi.A), , =, , (4) 256, , (1) 4, 125., , [4 0 0, , (4), , 367, , (4-16 30, , 0, , (4)2 4, , thesee

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1.32, 129. The inverse of a symmetric matrix (if it exists) is, (1) a symmetric matrix, , (2) a skew-symmetric matrix, , (3) a diagonal matrix, , (4), , none, , of these, , 130. The inverse of a skew-symmetric matrix of odd order is, (1) a symmetric matrix, , 3) a diagonalmatrix, , skew-symmetric matrix, , (2), , a, , (4), , does not exist, , 131. Let A, B, C be three square matrices of the same.order, such that whenever AR., =, , AC-, , B Cif A is, , 132., , [3 2, , IfA=0, ), , 1, , then A is, 1-1-26, , -267, , () 270 27., 133 The, , matrix A, , ) 270-27, , P, , =a, , IfA, , is, , a, , is, , n, , square matrix, , (3)p q+1, , satisfying the equation A2, , -, , 4A, , -, , 5I, , =, , -26, , (4)70, (4), , O then, , none, , A-, , of these, , =, , (4) (A-41), , )(A 41), , (2)(A-41)D, , (1) A-41, , 11-26, (3) 270 27J, , orthogonalif and only if, , (2) p-q, , (1) p + q=1, 134., , (4) skew-symmer, , (3) symmetric, , (2) non-singular, , (1) singular, , 135. If A is a non-singular square matrix satisfying the equation A - A + 21 = O then A, , 136., , If I, is the, , identity matrix, , 1, , 137., tan-, , of order 3, , x, , 3, then (1,), , =, , (4), , (3) 31, , (2) 1,, , (1)0, , (4) 50-A), , (3)+A), , (2) I+A, , (1) I-A, , e, , not necessarily, , tan-, , -tan, , -tan, , cos-sin8|, , cos, , sin, , -cose, , ()sin6-cose (2sin cose)sin, , -sin, , -cos, , (4), , none, , of these

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-, , 1.33-, , Matrices, 138., , 139., , The system o f equations which can be solved by cramer's rule nave, , (1) unique solution, , (2) two solutions, , (3) no solution, , (4) infinitely many, , The system of linear, , equations x +y +z 2, 2x, =, , +, , (2) - 1 <k <1, , 0, , 140. If det A, , =, , <2, (3)-2 <k, , 2y, , (4), , k=0, , (2), , unique solution, solution, , or, , solutions, , system, , +, of equations 7x 5y, , 13z, , +, , 4, , =0. 9x +, (2), , solutions, (1) infinitely many, , (3), 142., , The solution, , x, , (1), (3), 143, , 143., , unique solution x, , a, , 7, y, , =, , 7,, , x, , The, , of x +, =, , 10, z, , y=-, , system of, , y, , =1, 2x +, , + z, , 2y + 3z, , infinitely many, , 1-1, , 144., , 37,, , 1, y, , =, , x +, , 4y +, , 6,, , 9z, , which can, , be solved, , x, , =, , 7,, , y=, , 10,, , z, y =10,, , by matrix, , =2, , z, , = 3 13, =, , (4), , =4, , x, , =-3,, , inversion, , z, , 4, , =-4, , method, , nave, , ( 2 ) no solution, , (4) two solutions, solutions, , 0, , 1 thenadj.2A =, 3, =2, Ifadj. 2 1 -1, A, , I-10, , (1) 2 31, 21, 145., , unique, , (2), , (1) unique solution, (3), , a, , x-7,, , equations, , =, , no solution, , (4), , =4, , 10, z, , 11z, , +, , 2y, , solution, , =2, , has, , 3x - y *, , =, , 1, y =3, z, , =, , no, , infinite, , (4), , (3) no solution, e, , u, , *B has, 0 then the system of equations AX, , (1) infinite solutions, , n, , has a, , kz = 4, , +, , =3, 3x +, , y-z, , solution if,, (1) k, , solutions, , 2-2 0, (2)4, , do not, , 2, , 12, , 4, , [8 -8 0, , Then, , 16, , (4), , 16, , 8 4 4, , commute., matrices which, , (2) commute, , commute, , 0, , (3) 8, , 2-2, , -1, , B be two non-singular, Let A and, , (1), , 6, , 4-4, , 24, , 8, , 8, , -8, , A-, B-, , (3) AB=A. B-, , (4), , (3) 4, , (4) 1, , none, , of these, , 0, , 146., , IfA =4 then | 44|=, (1) 16, , (2) 8, , =(Radiant'sE, , =Chapter-1)

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1.34, , ANSWERS, 1. 2, , 2. 3, , 3., , 1, , 4., , 1, , 6. 4, , 7. 3, , 8. 3, , 9., , 3, , 11. 2, , 12. 2, , 13. 3, , 14., , 2, , 16. 4, , 17. 4, , 18. 2, , 19., , 1, , 21. 4, , 22. 4, , 23. 3, , 24., , 2, , 26., , 27. 4, , 28. 1, , 29., , 3, , 31. 2, , 32. 2, , 33. 1, , 34., , 3, , 35, , 36. 1, , 37. 2, , 38. 3, , 39., , 1, , 40. 4, , 41. 2, , 42. 2, , 43. 2, , 44., , 1, , 45., , 46. 2, , 47. 2, , 48. 3, , 49., , 3, , 50., , 51. 4, , 52. 4, , 53. 3, , 54., , 2, , 5.2, , 56. 4, , 57. 3, , 58. 4, , 59., , 4, , 60.3, , 61. 2, , 62., , 1, , 63.1, , 64., , 4, , 65. 1, , 66. 1, , 67. 1, , 68. 2, , 69., , 4, , 70.3, , 71. 4, , 72., , 1, , 73. 2, , 74., , 1, , 75. 3, , 76. 3, , 77., , 1, , 78. 4, , 79., , 4, , 80.2, , 81. 2, , 82. 3, , 83. 3, , 84., , 2, , 85, , 86. 4, , 87. 4, , 88. 1, , 89., , 3, , 90., , 91. 4, , 92. 3, , 93. 4, , 94., , 3, , 95., , 4, , 96. 4, , 97., , 1, , 98. 2, , 99., , 1, , 100., , 2, , 101. 4, , 102. 1, , 103. 4, , 104., , 2, , 105. 3, , 106. 1, , 107. 4, , 108. 1, , 109., , 3, , 110., , 111. 4, , 112. 2, , 113. 4, , 114., , 4, , 115.4, , 116. 3, , 117. 3, , 118. 4, , 119., , 4, , 120.4, , 121. 4, , 122. 3, , 123. 4, , 124., , 2, , 125., , 126. 2, , 127. 2, , 128. 1, , 129., , 1, , 131. 2, , 132. 3, , 133. 1, , 134., , 4, , 136. 2, , 137. 1, , 138. 1, , 139., , 1, , 141. 3, , 142. 3, , 143. 1, , 144., , 3, , 146., , (Chapter-1), , ., , 1, , Radiant's, , 10., 15, 20, , 25., 30., , 130., , 4, , 4, , 4, , 4, , 135. 4, 140., , 4, , 145. 2