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

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`

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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

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

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

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

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

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 |[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 A=|(1,sintheta,1),(-sintheta,1,sintheta),(-1,-sintheta,1)|, where ...

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  2. Prove the identities: |[a, b-c,c-b],[ a-c, b, c-a],[ a-b,b-a, c]| =(...

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

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  4. |((a^2+b^2)/c,c,c),(a,(b^2+c^2)/a,a),(b,b,(a^2+c^2)/b)| equal to : (A)...

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  5. Prove that identities: |[-bc,b^2+bc,c^2+bc],[a^2+ac,-ac,c^2+ac],[a^2+...

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  6. Without expanding, prove that |a b c x y z p q r|=|x y z p q r a b c|=...

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  7. If |[p, b, c],[ a, q, c],[ a, b, r]|=0, find the value of p/(p-a)+q/(...

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  8. Find the equation of the line joining A(1,3)a n dB(0,0) using determin...

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  9. If A(x1, y1),B(x2, y2) and C(x3,y3) are vertices of an equilateral ...

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  10. If f(x)=|0x-a x-b x+a0x-c x+b x+c0|,t h e n f(x)=0 (b) f(b)=0 (c) f...

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

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  12. Prove the identities: |[z, x, y],[ z^2,x^2,y^2],[z^4,x^4,y^4]|=|[x,...

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  13. Without expanding, show that the value of each of the determinants is ...

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  14. Without expanding, show that the value of each of the determinants is ...

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  15. Without expanding, show that the value of each of the determinants is ...

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  16. Without expanding, show that the value of each of the determinants is ...

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

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  18. Prove the identities: |[a, b, c],[ a-b,b-c,c-a],[ b+c,c+a, a+b]|=a^3+...

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  19. For any triangleABC, the value of determinant |[sin^2A,cotA,1],[sin^2B...

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  20. Without expanding, show that the value of each of the determinants is ...

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