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Factorize the following. [[x+a,b,c],[b,x...

Factorize the following. `[[x+a,b,c],[b,x+c,a],[c,a,x+b]]`

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Factorize the following. [[a,b,c],[b+c,c+a,a+b],[a^2,b^2,c^2]]

Prove the following: [[a,b,c],[b,c,a],[c,a,b]]=3abc-a^3-b^3-c^3

Prove that the following. [[a,b,c],[a^2,b^2,c^2],[bc,ca,ab]] =(b-c)(c-a)(a-b)(bc+ca+ab)

Prove that the following. [[b+c,a,a],[b,c+a,b],[c,c,a+b]] =4ab

Prove that the following. [[a,b,c],[x,y,z],[p,q,r]]=[[y,b,q],[x,a,p],[z,c,r]]=[[x,y,z],[p,q,r],[a,b,c]]

Prove the following: [[a+b+c,-c,-b],[-c,a+b+c,-a],[-b,-a,a+b+c]] =2(b+c)(c+a)(a+b)

Prove that the following. [[a,a^2,a^3],[b,b^2,b^3],[c,c^2,c^3]] = abc(a-b)(b-c)(c-a)

Prove that the following. [[1,1,1],[b+c,c+a,c+a],[b^2+c^2,c^2+a^2,a^2+b^2]] =(b-c)(c-a)(a-b)

Prove the following: [[b+c,a+b,a],[c+a,b+c,b],[a+b,c+a,c]] = a^3+b^3+c^3-3abc

Prove that the following. [[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=(a+b+c)^3

SHARAM PUBLICATION-MODEL QUESTION PAPER 12-EXERCISE
  1. Verify that A=[[a,b],[c,d]] satisfies the equation A^2-(a+d)A+(ad-bc...

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  2. Factorise the determinant |[x^3-a^3,x^2,x],[b^2-a^3,b^2,b],[c^3-a^3,c^...

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  3. Factorize the following. [[x+a,b,c],[b,x+c,a],[c,a,x+b]]

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  4. If A=[{:(3,1),(-1,2):}] then prove that A^(2)-5A+7I=O

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  5. Find the value of k if the function f(x) defined by f(x)={(2x-1,whenx<...

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  6. If sin y = x sin (a + y) then show that (dy)/(dx)=(sin^2(a+y))/(sina)

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  7. If y^2cot x = x^2 coty then find (dy)/(dx)

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  8. Find the intervals where function is increasing function y = cos x + s...

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  9. Find the equation of the normal to the curve 5x^2+3y^2=23 at (2,-1)

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  10. Integrate int sec xtanx.sqrt(tan^2x-3).dx

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  11. int(xe^x)/(1+x^2)dx

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  12. Evaluate int0^1[tan^-1x+x/(1+x^2)]dx

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  13. Find the area of region enclosed by y^2 = 4ax and x^2 = 4ay.

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  14. Find the particular solution of the following differential equation : ...

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  15. If the sum of two unit vectors is a unit vectors find the magnitude of...

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  16. If hati +hatj+hatk and 2hati -alphahatj+3hatk are orthogonal to each o...

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  17. Find the equation of the line through the point (2, 3, 5) and parallel...

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  18. Prove that the lines (x+4)/3=(y+6)/5=(z-1)/(-2) and 3x-2y+z+5=0=2x+3y...

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  19. Solve : tan^(-1)x+tan^(-1)((2x)/(1-x^2))=pi/2

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  20. If y=x^(sinx-cosx)+(x^(2)-1)/(x^(2)+1), then find (dy)/(dx)

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