19 .   A = 1 0 0 2 1 0 3 2 1   i f   U 1 , U 2   a n d   U 3   a r e   c o l u m n   m a t r i c e s   s a t i s f y i n g         A U 1 = 1 0 0 ,   A U 2 = 2 3 0   a n d   A U 3 = 2 3 1 ,   U   i s   3 × 3   m a t r i x   w h o s e   c o l u m n s   a r e         t h e n   a n s w e r   t h e   f o l l o w i n g   q u e s t i o n s   T h e   v a l u e   o f   U   i s   A   3                                               B   - 3                                                       C 3 2                                                     D 2

Dear Student,

Given A=100210321 ,AU1=100, AU2=230,AU3=231Now let U1=xyzSo,AU1=100210321xyz=100x2x+y3x+2y+z=100comparingx=12x+y=02+y=0y=-23x+2y+z=03+2×(-2)+z=03-4+z=0z=1 hence U1=1-21Similarly we do with AU2=100210321xyz=230x2x+y3x+2y+z=230comparingx=22x+y=34+y=3y=-13x+2y+z=06-2+z=0z=-4hence U2=2-1-4SimilarlyAU3=100210321xyz=231x2x+y3x+2y+z=231comparingx=22x+y=34+y=3y=-13x+2y+z=16-2+z=1z=-3hence U3=2-1-3it will be found that U=122-2-1-11-4-3

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