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Prove the identities: |{:(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`

A

2

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1

C

4

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3

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C
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OBJECTIVE RD SHARMA ENGLISH-DETERMINANTS-Exercise
  1. " if " |{:(b+c,,c+a,,a+b),(a+b,,b+c,,c+a),(c+a,,a+b,,b+c):}|=k |{:(a...

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  2. If A is a square matrix of order n such that its elements are polynomi...

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  3. Prove the identities: |{:(b^(2)+c^(2),,ab,,ac),(ab,,c^(2)+a^(2),,bc),...

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  4. a^(−1)+b^(−1)+c^(−1)=0 such that |[1+a,1,1,],[1,1+b,1,],[1,1,1+c,]| =△...

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  5. If alpha,beta,gamma are real numbers, then without expanding at any...

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  6. If A,B,C are the angles of triangle ABC, then the minimum value of |{:...

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  7. If x, y , z are in A.P., then the value of the det (A) is , where A ...

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  8. Find the number of real root of the equation |0x-a x-b x+a0x-c x+b x+c...

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  9. If a , b , c are distinct, then the value of x satisfying |0x^2-a x^3-...

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  10. Let the following system of equations {:(kx+y+z=1),(x+ky+z=k),(x+y+k...

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  11. Show that: |b^2+c^2a b a c b a c^2+a^2b c c a c b a^2+b^2|=4a^2b^2c^2

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  12. Let triangle =|[2a1b1, a1b2+a2b1, a1b3+a3b1], [a1b2+a2b1, 2a2b2, a2b3+...

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  13. If B is a non-sinfular matrix and A is square matrix, then det B^(-1)A...

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  14. If 0 lt theta lt pi and the system of equations (sin theta) x + y + ...

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  15. If the determinant |(b -c,c -a,a -b),(b' -c',c' -a',a' -b'),(b'' -c'',...

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  16. If a !=b, then the system of equation ax + by + bz = 0 bx + ay + bz ...

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  17. if |{:(1,,1,,1),(a,,b,,c),(a^(3),,b^(3),,c^(3)):}|= (a-b)(b-c)(c-a)(a+...

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  18. Show that a x+b y+r=0,b y+c z+p=0a n dc z+a x+q=0 are perpendicular to...

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  19. Consider the function f(x) = |{:(a^(2)+x,,ab,,ac),(ab,,b^(2)+x,,bc),(a...

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  20. The equation |(x-a,x-b,x-c),(x-b,x-a,x-c),(x-c,x-b,x-a)|=0 (a,b,c are ...

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