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Prove that, |(2a, a-b-c,2a),(2b,2b,b-c-a...

Prove that, `|(2a, a-b-c,2a),(2b,2b,b-c-a),(c-a-b,2c,2c)|=(a + b+c)^3`

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Prove that, |{:(-2a,a,a),(-2b,b,b),(c+a,b+c,-2c):}|=0

Prove that, |{:(6a,a,a),(12b,2b,2b),(9c,c,-2c):}|=0

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

Prove that: |[-2a, a+b,a+c],[ b+a,-2b,b+c],[c+a, c+b,-2c]|=4(a+b)(b+c)(c+a)

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

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

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)) |:}

Using properties of determinants , prove that, |{:(a,b,c),(b,c,a),(c,a,b):}|=-(a^3+b^3+c^3-3abc) and hence show that, |{:(2bc-a^2," "c^2," "b^2),(" "c^2,2ca-b^2," "a^2),(" "b^2," "a^2,2ab-c^2):}|=(a^3+b^3+c^3-3abc)^2

Prove that |a ,b+c, a^2,b, c+a, b^2,c, a+b, c^2|=-(a+b+c)xx(a-b)(b-c)(c- a)

Prove that {:|( a,a+b,a+b+c) ,( 2a,3a+2b,4a+3b+2c),( 3a,6a+3b,10a+6b+3c)|:}=a^(3)

UNITED BOOK HOUSE-SET 12-EXERCISE
  1. Find the intercept form of a plane with intercepts 2,3 and 4 on the x,...

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  2. A and B are two independent events with P(A) = 2/5 and P(B) = 1/3, eva...

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  3. The mean and variance of a binomial distribution are 4 and 3 respectiv...

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  4. If tan^(-1)x, tan^(-1)y and tan^(-1)z are in A.P, find the algebric re...

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  5. Prove that, the inverse of a given square matrix, if its exists, is un...

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  6. Prove that, |(2a, a-b-c,2a),(2b,2b,b-c-a),(c-a-b,2c,2c)|=(a + b+c)^3

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  7. If sqrt(1 -x^2) + sqrt(1-y^2) = a(x-y), show that, (dy)/(dx) = sqrtfra...

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  8. Evaluate: int (xdx)/[(x^2 - a^2)(b^2-x^2)] (b^2>a^2).

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  9. Evaluate: int(sqrt x dx)/sqrt(a^3 - x^3)

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  10. Solve:(dy)/(dx)-y/x + cosec (y/x)=0, given y = 0 when x = 1

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  11. Solve: y^2 + (x - 1/y)(dy)/(dx) = 0.

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  12. The position vectors of the points A and B are 2 veca + vecb and veca...

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  13. Evaluate: underset(0)overset(pi)int |sinx + cosx|dx

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  14. evaluate underset(0)overset(1)int e^(-x) dx

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  15. A packet, of 10 electronic components is known to include 3 defectives...

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  16. A random variable x follows binomial distribution with mean 3 and stan...

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  17. (b)answer any two questions : (i) a circular ink blot grows at the rat...

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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 vector equation of a line which passes throught the point wit...

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  20. Let vec n be a vector of magnitude 2sqrt 3 such that it makes equal ac...

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