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Show that |{:(a,b,c),(b,c,a),(c,a,b):}|^...

Show that `|{:(a,b,c),(b,c,a),(c,a,b):}|^2=|{:(2bc-a^(2),c^(2),b^(2)),(c^(2),2ac-b^(2),a^(2)),(b^(2),a^(2),2ab-c^(2)):}|=(a^(3)+b^(3)+c^(3)-3abc)^(2)`

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Show that |{:(a,b,c),(b,c,a),(c,a,b):}|=|{:(2bc-a^2,c^2,b^2),(c^2,2ac-b^2,a^2),(b^2,a^2,2ab-c^2):}|=(a^3+b^3+c^3-3abc)^2

|((b+c)^(2),a^(2),bc),((c+a)^(2),b^(2),ca),((a+b)^(2),c^(2),ab)|=

|(0,ab^(2),ac^(2)),(a^(2)b,0,bc^(2)),(a^(2)c,b^(2)c,0)|=

Show that |{:(1,a,a^2-bc),(1,b,b^2-ca),(1,c,c^2-ab):}|=0

Show that |{:(a,b,c),(a^(2),b^(2),c^(2)),(a^(2),b^(3),c^(3)):}|=abc(a-b)(b-c)(c-a)

|(0,c,b),(-c,0,a),(b,a,0)|-|(b^(2)+c^(2),ab,ac),(ab,c^(2)+a^(2),bc),(ac,bc,a^(2)+b^(2))|=

SRISIRI PUBLICATION-QUESTION PAPER -Section C
  1. Show that |{:(1,a^2,a^3),(1,b^2,b^3),(1,c^2,c^3):}| =(a-b)(b-c)(c-a)(a...

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  2. Show that |{:(a-b-c," "2a," "2a),(" "2b,b-c-a," "2b),(" "2c," "2...

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  3. Show that |{:(a,b,c),(b,c,a),(c,a,b):}|^2=|{:(2bc-a^(2),c^(2),b^(2)),(...

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  4. Find the value of x, if |(x-2,2x-3,3x-4),(x-4,2x-9,3x-16),(x-8,2x-27,3...

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  5. If A = [(cos theta, sin theta),(-sin theta, cos theta)] then show that...

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  6. By Cramer's rule, solve x-y+3z = 5, 4x+2y-z = 0, x+3y+z = 5.

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  7. By Matrix inverse method, solve 3x+4y+5z = 18, 2x-y+8z=13, 5x-2y+7z = ...

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  8. By Matrix inverse method, solve 3x+4y+5z = 18, 2x-y+8z=13, 5x-2y+7z = ...

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  9. Solve the system of equations x+y+z=3,2x+2y-z=3,x+y-z=1 by Gauss Jorda...

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  10. Examine the consistency of the following systems of equations x+y+z=1...

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  11. P.T the smaller angle theta between any two diagonals of a cube is giv...

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  12. If bar(a)=bar(i)-2bar(j)+3bar(k),bar(b)=2bar(i)+bar(j)+bar(k), bar(c)=...

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  13. If bar(a) = 2bar(i) + 3bar(j) + 4bar(k), bar(b) = bar(i) + bar(j) -bar...

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  14. Find the shortest distance between the skew lines . bar(r)=(6bar(i)...

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  15. If A=(1,-2,-1) , B=(4,0,-3),C= (1,2,-1),D=(2,-4,-5) then find distan...

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  16. If A+B+C= 180^(@), then show that sin 2A+ sin 2B+ sin 2C =4 sin A sin...

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  17. IF A,B,C are angles in the triangle, then prove that cosA+cosB-cosC=...

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  18. If A, B , C are angles in a triangle, then the sin ^(2)A+sin ^(2)B - s...

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  19. If A+B+ C =pi, then prove that cos ^(2) (A/2)+ cos ^(2) (B/2) +cos ^(2...

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  20. If A, B , C are angles of a triangle, then P. T sin ^(2) . (A)/(2)+ si...

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