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Prove without expanding |[a,a^2,bc],[b,...

Prove without expanding `|[a,a^2,bc],[b,b^2,ca],[c,c^2,ab]|=|[1,a^2,a^3],[1,b^2,b^3],[1,c^2,c^3]|`

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Prove that . |[1,a,a^2-bc],[1,b,b^2-ca],[1,c,c^2-ab]|=0

Without expanding show that |[1/a,1,bc],[1/b,1,ca],[1/c,1,ab]|=0

prove without expanding, |[(a-b),1,a],[b-c,1,b],[c-a,1,c]|=|[a,1,b],[b,1,c],[c,1,a]|

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

Prove that [[a^2,bc,c^2+ca],[a^2+ab,b^2,ca],[ab,b^2+bc,c^2]]= 4a^2b^2c^2 .

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

Without expanding prove that, |{:(1,bc,b+c),(1,ca,c+a),(1,ab,a+b):}|=|{:(1,a,a^(2)),(1,b,b^(2)),(1,c,c^(2)):}|

Without expanding prove that |{:(1,a,a^(2)-bc),(1,b,b^(2)-ca),(1,c,c^(2)-ab):}|=0

Without expanding prove that, |{:(b^2c^2,bc,b+c),(c^2a^2,ca,c+a),(a^2b^2,ab,a+b):}|=0

Using the property of determinants and without expanding {:|( -a^(2) , ab,ac),( ba,-b^(2) , bc) ,( ca, cb, -c^(2)) |:} =4a^(2) b^(2) c^(2)

UNITED BOOK HOUSE-SET 9-EXERCISE
  1. The mean of the binomial distribution with parameters n and p is

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  2. Prove that sin cosec^(-1)cot(tan^(-1)x) =x

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  3. Prove without expanding |[a,a^2,bc],[b,b^2,ca],[c,c^2,ab]|=|[1,a^2,a^...

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  4. Find the matrix A , when A^(-1) = [[cos theta, sin theta],[-sin theta,...

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  5. Evaluate : underset(x to e)"Lt"(logx-1)/(x-e)

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  6. Examine whether Rolle's theorem is applicable to the function f(x) = c...

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  7. int((x^2+sin^2x)/(1+x^2))sec^2xdx is equals

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  8. Find the degree and order of the differetial equation 1+((d^3y)/(dx^3)...

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  9. answer any three questions: (iii) if x>0 ,y>0 and xy=25, then find the...

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  10. Find the value of tan 44^@, given tan1^@ = 0.01745.

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  11. Find the direction cosines and direction ratios of the vector 2 hati +...

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  12. The cartesian equation of a line AB is (3-x)/1=(y+2)/-2=(z-5)/4. Find ...

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  13. If P(barA uu bar B)= 5/6, P(A)= 1/2 and P(bar B)= 2/3 show that A and ...

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  14. Find the probability that in a family of 4 children there will be at l...

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  15. answer any one question : (ii) prove that , tan(pi/4 +1/2 (cos ^(-1) (...

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  16. If A = [[3,1],[-1,2]],I= [[1,0],[0,1]] and O = [[0,0],[0,0]] show that...

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  17. Show that, A = 1/3[[1,2,2],[2,1,-1],[-2,2,-1]] are orthogonal matrix a...

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  18. Solve for x |x-2 , 2x-3, 3x-4,x-4 ,2x-9, 3x-16 ,x-8, 2x-27, 3x-64|=0.

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  19. Show that the following determinant is a perfect square |[1,a,a^2],[a^...

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  20. If siny = x sin(a+y) then show that (dy)/(dx)= (sina)/(1-2xcos a+x^2).

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