using the properties of determinant find the value of x, if the value of the following determinant is zero
 
 
 x-2    2x-3     3x-4
 
 x-4    2x-9     3x-16
 
 x-8    2x-27   3x-64 

Asked by ppratim02 | 4th Jul, 2016, 05:32: PM

Expert Answer:

begin mathsize 12px style open vertical bar table row cell straight x minus 2 end cell cell 2 straight x minus 3 end cell cell 3 straight x minus 4 end cell row cell straight x minus 4 end cell cell 2 straight x minus 9 end cell cell 3 straight x minus 16 end cell row cell straight x minus 8 end cell cell 2 straight x minus 27 end cell cell 3 straight x minus 64 end cell end table close vertical bar equals 0
straight R subscript 2 rightwards arrow straight R subscript 2 minus straight R subscript 3
open vertical bar table row cell straight x minus 2 end cell cell 2 straight x minus 3 end cell cell 3 straight x minus 4 end cell row 4 18 48 row cell straight x minus 8 end cell cell space space space 2 straight x minus 27 end cell cell space space 3 straight x minus 64 end cell end table close vertical bar equals 0
straight R subscript 3 rightwards arrow straight R subscript 3 minus straight R subscript 1
open vertical bar table row cell straight x minus 2 end cell cell 2 straight x minus 3 end cell cell 3 straight x minus 4 end cell row 4 18 48 row cell negative 6 end cell cell space space space minus 24 end cell cell space minus 60 end cell end table close vertical bar equals 0
rightwards double arrow left parenthesis straight x minus 2 right parenthesis left square bracket negative 1080 plus 1152 right square bracket minus left parenthesis 2 straight x minus 3 right parenthesis left square bracket negative 240 plus 288 right square bracket plus left parenthesis 3 straight x minus 4 right parenthesis left square bracket negative 96 plus 108 right square bracket equals 0
rightwards double arrow 72 straight x minus 144 minus 96 straight x plus 144 plus 36 straight x minus 48 equals 0
rightwards double arrow 12 straight x equals 48
rightwards double arrow straight x equals 4 end style

Answered by Rebecca Fernandes | 5th Jul, 2016, 01:09: PM