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Prove the identities: |[b^2+c^2,ab, ac]...

Prove the identities: `|[b^2+c^2,ab, ac],[ba,c^2+a^2,bc],[ca, cb ,a^2+b^2]|=4a^2b^2c^2`

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Prove the identity: |[b^2+c^2,ab, ac],[ba,c^2+a^2,bc],[ca, cb ,a^2+b^2]|=4a^2b^2c^2

Show that |[b^2+c^2,ab,ac],[ba,c^2+a^2,bc],[ca,cb,a^2+b^2]|=4a^2b^2c^2

Show that |[b^2+c^2,ab,ac],[ba,c^2+a^2,bc],[ca,cb,a^2+b^2]|=4a^2b^2c^2

abs([-a^2,ab,ac],[ba,-b^2,bc],[ca,cb,-c^2]) = 4a^2.b^2.c^2

|[x^2+a^2,ab,ac] , [ab,x^2+b^2,bc] , [ac,bc,x^2+c^2]|=

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 the identities: |{:(b^(2)+c^(2),,ab,,ac),(ab,,c^(2)+a^(2),,bc),(ca,,bc,,a^(2)+b^(2)):}|=4a^2b^2c^2

Prove the identities: |[a^2,a^2-(b-c)^2,b c], [b^2,b^2-(c-a)^2,c a],[ c^2,c^2-(a-b)^2,a b]|=(a-b)(b-c)(c-a)(a+b+c)(a^2+b^2+c^2)

Prove that identities: |[-bc,b^2+bc,c^2+bc],[a^2+ac,-ac,c^2+ac],[a^2+ab,b^2+ab,-ab]|=(a b+b c+a c)^3

Using properties of determinants, prove that |[a^2, bc, ac+c^2] , [a^2+ab, b^2, ac] , [ab, b^2+bc, c^2]| = 4a^2b^2c^2

CENGAGE ENGLISH-DETERMINANTS-All Questions
  1. The value of |-1 2 1 3+2sqrt(2) 2+2sqrt(2) 1 3-2sqrt(2...

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  2. Find the following system of equations is consistent, (a+1)^3x+(a+2...

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  3. Prove the identities: |[b^2+c^2,ab, ac],[ba,c^2+a^2,bc],[ca, cb ,a^2+...

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  4. If |1 1 1a b c a^3b^2c^3|=(a-b)(b-c)(c-a)(a+b+c),w h e r ea ,b ,c are...

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  5. Prove that [[1+a^2+a^4, 1+a b+a^2b^2 ,1+a c+a^2c^2],[ 1+a b+a^2b^2, 1+...

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  6. The determinant |y^2-x y x^2a b c a ' b ' c '| is equal to a.|b x+a ...

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  7. If x , y , z are in A.P. , then the value of the determinant |[a+2,...

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  8. Prove that |{:((b+x)(c+x),,(c+x)(a+x),,(a+x)(b+x)),((b+y)(c+y) ,,(c+y)...

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  9. If a+b+c=0, one root of [[a-x, c, b],[c, b-x, a],[ b, a, c-x]]=0 is ...

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  10. Factorize the following |[3,a+b+c,a^3+b^3+c^3],[a+b+c,a^2+b^2+c^2,a^4+...

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  11. Let {D1, D2, D3 ,Dn} be the set of third order determinant that can be...

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  12. If g(x)-(f(x))/((x-a)(x-b)(x-c)),w h e r ef(x) is a polynomial of d...

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  13. If the equation 2x+3y+1=0,3x+y-2=0, and a x+2y-b=0 are consistent, t...

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  14. If w is a complex cube root of unity, then value of =|[a1+b1w, a1w^2+b...

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  15. Let f(x)=|[cos(x+x^2),sin(x+x^2),-cos(x+x^2)],[sin(x-x^2),cos(x-x^2), ...

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  16. Which of the following has/have value equal to zero? |8 2 7 12 3 5 16 ...

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  17. If f(x),g(x)a n dh(x) are three polynomial of degree 2, then prove t...

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

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  19. 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)d...

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  20. In triangle A B C , if |1, 1, ,1,cotA/2,cotB/2,cotC/2,tanB/2+tanC/2,ta...

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