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Show that: |[a, b-c,c+b], [a+c, b, c-a]...

Show that: `|[a, b-c,c+b], [a+c, b, c-a],[a-b,b+a, c]|`=`(a+b+c)(a^2+b^2+c^2)dot`

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If =|[a b c, b^2c,c^2b],[ a b c,c^2a, c a^2],[a b c, a^2b,b^2a]|=0,(a ,b ,c in R) and are all different and nonzero), then prove that a+b+c=0.

Show that: abs(((b+c)^2,a^2,bc) , ((c+a)^2,b^2,ca) , ((a+b)^2,c^2,ab))=(a^2+b^2+c^2)(a+b+c)(b-c)(c-a)(a-b)

CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. If f(x),g(x) and h(x) are three polynomials of degree 2, then prove th...

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  2. If a ,b ,c are in G.P. with common ratio r1a n dalpha,beta,gamma are i...

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  3. Show that: |[a, b-c,c+b], [a+c, b, c-a],[a-b,b+a, c]|=(a+b+c)(a^2+b^2...

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  4. In triangle A B C , if |[1, 1, 1],[cot(A/2),cot(B/2),cot(C/2)],[tan(B/...

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  5. If a ,b ,c ,d ,e, and fare in G.P. then the value of |((a^2),(d^2),x)...

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  6. Prove that: |[(b+c)^2,a^2,a^2],[b^2,(c+a)^2,b^2],[c^2,c^2,(a+b)^2]|=2a...

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  7. If xi=ai bi ci,i=1,2,3 are three-digit positive integer such that ea...

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  8. The system of linear equations x+lambday-z=0, lambdax-y-z=0, x+y-lam...

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  9. If a , b ,c are all different and |[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^...

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  10. If p q r!=0 and the system of equation (p+a)x+b y+c z=0, a x+(q+b)y+c...

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  11. If c<1 and the system of equations x+y-1=0,2x-y-c=0,a n d -b x+3b y-c=...

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  12. Prove that |x^2x^2-(y-z)^2y z y^2y^2-(z-x)^2z x z^2z^2-(x-y)^2x y|=(...

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  13. If a, b and c are real numbers, and Delta=|[b+c,c+a,a+b],[c+a,a+b,b+c]...

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  14. If a , b , c are non-zero, then the system of equations (alpha+a)x+alp...

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  15. Prove that |a ,b+c, a^2,b, c+a, b^2,c, a+b, c^2|=-(a+b+c)xx(a-b)(b-c)...

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

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  17. Using the properties of determinants, prove that following |(a-b-c,2a,...

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  18. If a1,a2,a3,.....an.... are in G.P. then the determinant Delta=|[log a...

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  19. Prove that,abs((a^2+1,ab,ac),(ab,b^2+1,bc),(ca,cb,c^2+1))=1+a^2+b^2+c^...

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

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