great excuser faculty which always any time making excuses that due to paucity of time unable to solve ur query - Maths - Determinants

Question

great excuser faculty which always any time making excuses that
due to paucity of time unable to solve ur query i dont lke this
type of great excuse
solve my doubt
if a,b,c r positive and unequal show that this value is negative
3abc-( a cube+ b cube + c cube )
2- how to find adjoint of a and explain the best another way of
solving this question example 32 of miscellaneous of ncert
explain singular and nonsingular matrix

Brijendra P. · Accepted Answer

1) 
if a,b,c r positive and unequal show that this value is negative
3abc-( a cube+ b cube + c cube )

Proof-

= abcbcacab = a+b+cbca+b+ccaa+b+cab Applying [
c1→(c1+c2+c3)]=(a+b+c) 1bc1ca1abNow solving we get,
=(a+b+c)[(c-b)(b-c)-(a-b)(a-c)]=(a+b+c)(-a2 -b2 - c2 +ab +
bc+ca)=-(a+b+c)(a2 +b2 +c2 -ab - bc-ca)And it is the direct formula
of a3 +b3+c3 -3abc =(a+b+c)(a2 +b2 +c2 -ab - bc-ca)So the above
expression is negative quantity
3) Here is the link for singular and non singular matrix

https://www meritnation
com/ask-answer/question/we-mean-by-singular-or-non-singular-matrix-irrespectiv/determinants/631734

2) â€‹Here is the link to answer for your query
for finding adjoint of a matrix:

https://www meritnation
com/ask-answer/question/sir-how-find-a-adjoint-of-any-matrix/matrices/6280163