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 

Asked by lekhakarthikeyan | 27th Dec, 2018, 02:23: AM

Expert Answer:

begin mathsize 16px style 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 squared plus ac end cell cell straight b cubed end cell row 1 cell straight c squared plus ab end cell cell straight c cubed end cell end table close vertical bar
Use space steps space below colon
straight R subscript 2 rightwards arrow straight R subscript 2 space minus space straight R subscript 1 space and space straight R subscript 3 rightwards arrow straight R subscript 3 space minus space straight R subscript 1 space space space space
Take space left parenthesis straight b minus straight a right parenthesis space from space straight R subscript 2 space and space Take space left parenthesis straight c minus straight a right parenthesis space from space straight R subscript 3 space
Expand space determinant space we space get space
minus left parenthesis straight a minus straight b right parenthesis left parenthesis straight b minus straight c right parenthesis left parenthesis straight c minus straight a right parenthesis left parenthesis straight a squared plus straight b squared plus straight c squared right parenthesis



NOTE colon space
Question space should space be
Prove space that space 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 squared plus ac end cell cell straight b cubed end cell row 1 cell straight c squared plus ab end cell cell straight c cubed end cell end table close vertical bar equals negative left parenthesis straight a minus straight b right parenthesis left parenthesis straight b minus straight c right parenthesis left parenthesis straight c minus straight a right parenthesis left parenthesis straight a squared plus straight b squared plus straight c squared right parenthesis end style

Answered by Sneha shidid | 27th Dec, 2018, 12:15: PM