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If A=|[1, 1, 1],[a, b, c],[ a^2,b^2,c^2]...

If `A=|[1, 1, 1],[a, b, c],[ a^2,b^2,c^2]|` , `B=|[1,bc, a],[1,ca, b],[1,ab, c]|` , then

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If A=[[1, 1,-1],[ 2, 0, 3],[ 3,-1, 2]] , B=[[1, 3],[0,2],[-1, 4]] and C=[[1,2, 3,-4],[ 2, 0,-2, 1]] , find A(BC), (AB)C and show that (A B)C = A(B C) .

If A=|(1,1,1),(a,b,c),(a^3,b^3,c^3)|, B=|(1,1,1),(a^2,b^2,c^2),(a^3,b^3,c^3)|, C=|(a,b,c),(a^2,b^2,c^2),(a^3,b^3,c^3)| , then which relation is correct :

Show that |[a ,b ,c],[ a^2,b^2,c^2],[bc, ca, ab]|=|[1, 1, 1],[a^2,b^2,c^2],[a^3,b^3,c^3]|=(a-b)(b-c)(c-a)(a b+b c+c a) .

|[bc-a^2,ca-b^2,ab-c^2],[ca-b^2,ab-c^2,bc-a^2],[ab-c^2,bc-a^2,ca-b^2]|=|[a,b,c],[b,c,a],[c,a,b]|^2

By using properties of determinants. Show that: (i) |[1,a, a^2],[ 1,b,b^2],[ 1,c,c^2]|=(a-b)(b-c)(c-a) (ii) |[1, 1, 1],[a, b, c],[ a^3,b^3,c^3]|=(a-b)(b-c)(c-a)(a+b+c)

Prove that =|1 1 1a b c b c+a^2a c+b^2a b+c^2|=2(a-b)(b-c)(c-a)

Show that |[1,a,a^2],[1,b,b^2],[1,c,c^2]|=(a-b)(b-c)(c-a)

Evaluate the following: |[1,,a^2-bc],[1, b,b^2-ac],[1,c,c^2-ab]|

Using properties of determinants, prove the following: |[a^2 + 1,ab, ac], [ab,b^2 + 1,b c],[ca, cb, c^2+1]|=1+a^2+b^2+c^2

Prove that |[a^2+1,ab,ac],[ab,b^2+1,bc],[ac,bc,c^2+1]|=1+a^2+b^2+c^2

RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. Let |[x,2,x],[x^2,x,6],[x,x,6]|=a x^4+b x^3+c x^2+dx+edot Then, the va...

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  2. The value of the determinant |a^2a1cosn xcos(n+a)xcos(n+2)xsinn xsin(n...

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  3. If A=|[1, 1, 1],[a, b, c],[ a^2,b^2,c^2]| , B=|[1,bc, a],[1,ca, b],[1,...

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  4. If Dk=|(1, n, n),(2k, n^2+n+1,n^2+n),(2k-1,n^2,n^2+n+1)| and sum(k=1)^...

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  5. Let |[x^2+3x,x-1,x+3],[x+1,-2x,x-4],[x-3,x+4, 3x]|=a x^4+b x^3+c x^2+e...

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  6. Using the factor theorem it is found that a+b , b+c and c+a are three ...

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  7. If a ,b ,c are different, then the value of |[0,x^2-a, x^3-b], [x^2+a,...

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  8. If the determinant |(a ,b,2aalpha+3b),(b, c,2balpha+3c),(2aalpha+3b,2b...

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  9. If 1.omega, omega^2 are the roots of unity, then Delta=|(1,omega^n,ome...

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  10. If Ar=|(1,r,2^r),(2,n,n^2),(n,(n(n+1))/2 ,2^(n+1))| , then the value o...

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

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  12. The value of |[5^2 ,5^3, 5^4], [5^3, 5^4, 5^5], [5^4, 5^5, 5^6]| is (a...

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  13. |[(log)3 512,(log)4 3],[(log)3 8,(log)4 9]|xx|[(log)2 3,(log)8 3],[(lo...

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  14. If a, b, c, are in A.P, then the determinant|[x+2,x+3,x+2a], [x+3,x+4,...

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  15. If A+B+C=pi, then the value of |"sin"(A+B+C)sin(A+C)cosC-sinB0tanCcos...

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  16. The number of distinct real roots of |{:(cosec x, secx, secx), (secx...

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  17. Let A=|[1,sintheta,1],[-sintheta,1,sintheta],[-1,-sintheta,1]|, where ...

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  18. If |[2x,5], [8,x]|=|[6,-2], [7, 3]| , then x= (a) 3 (b) +-3 (c) +-6 (...

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  19. If f(x)=|[0,x-a, x-b], [x+a,0,x-c], [x+b, x+c,0]|,t h e n (a)f(a)=0 ...

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  20. The value of the determinant |[a-b,b+c, a], [b-a, c+a, b], [c-a, a+b...

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