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By using properties of determinants. Sho...

By using properties of determinants. Show that: `|1+a^2-b^2; 2ab; -2b: 2ab;1-a^2+b^2; 2a: 2b;-2a;1-a^2-b^2|=(1+a^2+b^2)^3`

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|{:(" "1+a^2-b^2," "2ab," "-2b),(" "2ab,1-a^2+b^2," "2a),(" "2b," "-2a,1-a^2-b^2):}|=(1+a^2+b^2)^3

The value of the determinant |(1+a^(2)-b^(2),2ab,-2b),(2ab,1-a^(2)+b^(2),2a),(2b,-2a,1-a^(2)-b^(2))| is equal to

Using the properties of determinants, prove that following |(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)|=(a+b+c)^3

By using properties of determinants , show that : (i) {:|( 1,a,a^(2)),( 1,b,b^(2)),( 1,c,c^(2))|:}=(a-b)(b-c) (c-a) (ii) {:|( 1,1,1),( a,b,c) ,(a^(3) , b^(3), c^(3))|:} =( a-b) (b-c)( c-a) (a+b+c)

Using properties of determinants prove that, |{:((b+c)^(2),a^(2),a^(2)),(b^(2),(c+a)^(2),b^(2)),(c^(2),c^(2),(a+b)^(2)):}|=2abc(a+b+c)^(3)

Using formula let's show that. (3a-4b)^2 + 24ab = 9a^2 +16b^2

If a,b,c are in continued proportion, then show that 1/b^2= 1/(b^2-a^2)+1/(b^2-c^2)

Without expanding the determinant, prove that {:|( 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)) |:}

prove that , |{:(2ab,a^2,b^2),(a^2,b^2,2ab),(b^2,2ab,a^2):}|=-(a^3+b^3)^2

Prove that |[2ab,a^2,b^2],[a^2,b^2,2ab],[b^2,2ab,a^2]|=-(a^3+b^3)^2 .

UNITED BOOK HOUSE-SET 14-EXERCISE
  1. Using direction ratios show that the points (2,6,3),(1,2,7) and (3,10,...

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  2. Find the equation of the plane which passing through the point hati + ...

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  3. For three mutually exclusive events X,Y and Z it is given that P(x) = ...

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  4. A discrete random variable X has the following distribution: find a.

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  5. If xy = 1 + a^2 then show that, tan^(-1) [1/(a + x)]+tan^(-1) [1/(a+y)...

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  6. By using properties of determinants. Show that: |1+a^2-b^2; 2ab; -2b: ...

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  7. If y = f(x^2) and f'(x) = sqrt (3x^2+1), find [(dy)/(dx)](x=2)

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  8. If y= (tan^(-1)x)^2, then show that (1+x^2)^2(d^2y)/(dx^2)+2x(1+x^2)(d...

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  9. Prove that, int(cos 5x + cos4x)/(1-2cos 3x)dx= -(1/2 sin2x + sinx)+c

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  10. Solve:(dy)/(dx)=(3x + 4y+1)/(-4x+2y-3)

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  11. Solve:(x^2-1)(dy)/(dx) + 2xy = 2/(x^2-1)

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  12. vec a = hati +hatj + hatk and vecb = -2hati +hatj +2hatk represent two...

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  13. Find the vector alpha which is perpendicular to both 4 hati + 5hatj -...

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  14. Show that: overset(1)underset(0)int (log(1+x)/(1+x^2))dx= pi/8 log 2.

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  15. Evaluate:underset(n rarr infty)lim 1/n[sin (pi/(2n)) +sin((2pi)/(2n))+...

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  16. A random variable X has the following probability function: Calculate...

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  17. A random variable X has the following probability function: Find P(x ...

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  18. A random variable X has the following probability function: Calculate...

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  19. Show that the maximum value of 2x + 1/(2x)is less than its minimum val...

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  20. answer any one question : (ii) find the equation of the line which is...

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