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Let triangle =|[2a1b1, a1b2+a2b1, a1b3+a...

Let `triangle =|[2a_1b_1, a_1b_2+a_2b_1, a_1b_3+a_3b_1], [a_1b_2+a_2b_1, 2a_2b_2, a_2b_3+a_3b_2], [a_1b_3+a_3b_1, a_3b_2+a_2b_3, 2a_3b_3]|` . Expressing `` as the product of two determinants, show that `triangle=0`

A

1

B

`-1`

C

0

D

`a_(1) a_(2) a_(3) b_(1) b_(2) b_(3)`

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The correct Answer is:
C
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OBJECTIVE RD SHARMA ENGLISH-DETERMINANTS-Exercise
  1. Let the following system of equations {:(kx+y+z=1),(x+ky+z=k),(x+y+k...

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

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

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

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

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

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

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

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  11. 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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  12. Let A = [(1,sin theta,1),(- sin theta,1,sin theta),(-1,-sin theta,1)],...

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  13. If a,b,c are non-zero real number such that |(bc,ca,ab),(ca,ab,bc),(ab...

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  14. The value of the determinant |{:(ka,,k^(2)+a^(2),,1),(kb,,k^(2)+b^(2)...

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  15. The system of simulataneous equations kx + 2y -z = 1 (k -1) y -2z ...

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  16. The value of the determinant |(1,omega^(3),omega^(5)),(omega^(3),1,ome...

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  17. If a,b,c are non-zero real number such that |(bc,ca,ab),(ca,ab,bc),(ab...

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  18. If the system of equations x + ay + az = 0 bx + y + bz = 0 cx + ...

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  19. The determinant D=|{:(cos(alpha+beta),-sin(alpha+beta),cos2beta),(sina...

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  20. If omega is a cube root of unity, then Root of polynomial is |(x + 1...

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