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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 19-EXERCISE
  1. If x>1/2, show that the function f(x) = x(4x^2 - 3) is steadily increa...

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  2. If |veca| = sqrt3,|vecb| = 2 and veca.vecb = sqrt6, then find the angl...

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  3. If the line (x-2)/(6) = (y-1)/(lambda) = (z+5)/(-4) is perpendicular t...

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  4. The probability that A hits a target is 1/3 and the probability that B...

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  5. An unbiased coin is toosed 7 times. Find the probability of getting an...

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

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  7. Solve : |(x+4, 2x,2x),(2x , x+4, 2x),(2x, 2x, x+4)| = 0

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

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  9. If y^(1/3) + y^(-1/3) = 2x, prove that (x^2 - 1)y2 + xy1 = 9y.

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  10. Evaluate : int(loge(x+1))/((x+1)^2) dx

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  11. Evaluate :int(5^(5^(5^x)cdot 5^(5^(x))cdot 5^x))dx

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  12. Solve the differential equation: (1+y^2)+(x - e^(tan^-1 y) )dy/dx = 0

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  13. Find the unit vector which is perpendicular to both veca = 2hati + 3ha...

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  14. If veca = hati + hatj + hatk , vecb = hatj - hatk then find a vector v...

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  15. Evaluate: underset(nrarralpha)Lt[1/(sqrt(2n-1^2)) +1/(sqrt(4n-2^2))+1/...

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  16. Evaluate : int(0)^(pi/4) (sin^2xcos^2xdx)/((sin^3x+cos^3x)^2)

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  17. A discreate random variable x has the following probability distributi...

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  18. answer any two questions :(iii) if the straight line lx+my=n be a norm...

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  19. Find the area enclosed by the curves x^2=y , y=x+2 and x-axis

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  20. A 5 ft long man walks away from the foot of a 12 1/2 ft high lamp post...

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