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If a,b and c are real numbers, and De...

If a,b and c are real numbers, and
`Delta ={:[( b+c,C+a,a+b),( c+a,a+b,b+c),( a+b,b+c,c+a) ]:}=0`
Show that either `a+b+c=0 "or" a= b= c . `

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CENGAGE-DETERMINANTS-All Questions
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  2. Prove that |(x^2,x^2-(y-z)^2,yz),(y^2,y^2-(z-x)^2,zx),(z^2,z^2-(x-y)^2...

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  5. Prove that |a b+c a^2b c+a b^2c a+b c^2|=-(a+b+c)xx(a-b)(b-c)(c-a)dot

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  6. If a >0 and discriminant of a x^2+2b x+c is negative, then |[a,b,ax+...

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  7. If |(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)|=(a+b+c) xx(x + a + b...

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  9. By using properties of determinants , show that : {:[( a^(2) + 1, a...

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  10. Let vec ar=xr hat i+yr hat j+zr hat k ,r=1,2,3 be three mutually per...

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  11. The number of distinct real roots of |[sinx,cosx,cosx],[cosx,sinx,cosx...

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  12. Let a ,b ,c be real numbers with a^2+b^2+c^2=1. Show that the eq...

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  14. If plambda^4+qlambda^3+rlambda^2+slambda+t=|[lambda^2+3lambda, lambda-...

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  15. Find the value of lambda if 2x^2+7x y+3y^2+8x+14 t+lambda=0 represents...

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  16. If x ,y ,z are different from zero and "Delta"=|[a, b-y ,c-z],[ a-x, ...

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  17. If A , B ,C are angles of a triangles, then the value of |[e^(2i A),...

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  18. For the equation |[1,x,x^2],[x^2, 1,x],[x,x^2, 1]|=0, There are exa...

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  19. Let "Delta"r=|r-1n6(r-1)^2 2n^2 4n-2(r-1)^2 3n^3 3n^2-3n|dot Show that...

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  20. Let m be a positive integer and Deltar=|[2r-1,.^mCr,1],[m^2-1,2^m,m+1]...

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