The following question is from the lesson matrices .
if Y = det 1          X                  X+1
                 2x     X(X-1)         (X+1)X
          3X(X-1)  X(X-1)(X-2)  (X+1)X(X-1)
 
REPRESENT S WHICH OF THE FOLLOWING AND WHY:
1.STRAIGHT LINE PASSING THROUGH ORIGIN.
2.A STRAIGHT LINE NOT PASSING THROUGH ORIGIN.
3.A PARABOLA
4. A HYPERBOLA

Asked by Sai Seravan Bodipudi | 12th Jun, 2015, 07:03: PM

Expert Answer:

Start by simplifying the determinant.
open vertical bar table row 1 x cell x plus 1 end cell row cell 2 x end cell cell x open parentheses x minus 1 close parentheses end cell cell open parentheses x plus 1 close parentheses x end cell row cell 3 x open parentheses x minus 1 close parentheses end cell cell x open parentheses x minus 1 close parentheses open parentheses x minus 2 close parentheses end cell cell open parentheses x plus 1 close parentheses open parentheses x close parentheses open parentheses x minus 1 close parentheses end cell end table close vertical bar equals x open parentheses x plus 1 close parentheses open vertical bar table row 1 1 1 row cell 2 x end cell cell open parentheses x minus 1 close parentheses end cell x row cell 3 x open parentheses x minus 1 close parentheses end cell cell open parentheses x minus 1 close parentheses open parentheses x minus 2 close parentheses end cell cell open parentheses x close parentheses open parentheses x minus 1 close parentheses end cell end table close vertical bar space open parentheses t a k i n g space apostrophe x apostrophe space a n d space apostrophe x plus 1 apostrophe space c o m m o n space f r o m space C subscript 2 space a n d space C subscript 3 space r e s p e c t i v e l y. close parentheses equals x open parentheses x plus 1 close parentheses open parentheses x minus 1 close parentheses open vertical bar table row 1 1 1 row cell 2 x end cell cell open parentheses x minus 1 close parentheses end cell x row cell 3 x end cell cell open parentheses x minus 2 close parentheses end cell x end table close vertical bar space open parentheses t a k i n g space apostrophe x minus 1 apostrophe space c o m m o n space f r o m space R subscript 3 close parentheses equals x open parentheses x plus 1 close parentheses open parentheses x minus 1 close parentheses open vertical bar table row 0 0 1 row cell x plus 1 end cell cell negative 1 end cell x row cell 2 x plus 2 end cell cell negative 2 end cell x end table close vertical bar space space space space open parentheses table row cell C subscript 1 leftwards arrow C subscript 1 minus C subscript 2 end cell row cell C subscript 2 leftwards arrow C subscript 2 minus C subscript 3 end cell end table close parentheses
N o w space e x p a n d i n g space t h e space d e t e r m i n a n t comma space w e space g e t x open parentheses x plus 1 close parentheses open parentheses x minus 1 close parentheses open square brackets negative 2 open parentheses x plus 1 close parentheses plus 2 x plus 2 close square brackets equals x open parentheses x plus 1 close parentheses open parentheses x minus 1 close parentheses cross times 0 equals 0 H e n c e comma space w e space g e t space y equals 0 comma space w h i c h space i s space e q u a t i o n space o f space t h e space X minus a x i s. space I t space p a s s e s space t h r o u g h space o r i g i n. H e n c e comma space o p t i o n space 1 space i s space c o r r e c t.

Answered by satyajit samal | 14th Jun, 2015, 08:28: AM