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CBSE Class 12-science Answered

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 | 04 Jul, 2016, 05:32: PM
answered-by-expert 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 | 05 Jul, 2016, 01:09: PM

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CBSE 12-science - Maths
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Using the properties of determinants,prove that  open vertical bar table row 1 cell straight a squared plus bc end cell cell straight a cubed end cell row 1 cell straight b plus ca end cell cell straight b cubed end cell row 1 cell straight i squared plus ab end cell cell straight C cubed end cell end table close vertical bar = -(a-b)(b-c)(c-a)(a3+b3+c3)   Pls note it is c instead of  i 
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CBSE 12-science - Maths
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CBSE 12-science - Maths
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