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Show that: |1+a^2-b^2 2a b-2b2a b1-a^2+b...

Show that: |1+a^2-b^2 2a b-2b2a b1-a^2+b^2 2a2b-2a1-a^2-b^2|=(1+a^2+b^2)^3`

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By using properties of determinants. Show that: |[1+a^2-b^2, 2a b,-2b],[2a b,1-a^2+b^2, 2a],[2b,-2a,1-a^2-b^2]|=(1+a^2+b^2)^3

Using properties of determinants, prove 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)

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)

Simplify: a^2b(a-b^2)+a b^2(4a b-2a^2)-a^3b(1-2b)

If a, b and c are in G.P. then prove that 1 a 2 - b 2 + 1 b 2 = 1 b 2 - c 2 . 1/(a^2-b^2)+1/(b^2)=1/(b^2-c^2)dot

By using properties of determinants. Show that: |[a^2+1,a b, a c],[ a b,b^2+1,b c],[c a, c b, c^2+1]|=(1+a^2+b^2+c^2)

Prove that [[1+a^2+a^4, 1+a b+a^2b^2 ,1+a c+a^2c^2],[ 1+a b+a^2b^2, 1+b^2+b^4, 1+b c+b^2c^2],[ 1+a c+a^2c^2, 1+b c+b^2c^2, 1+c^2+c^2]]=(a-b)^2(b-c)^2(c-a)^2

Factorise : a^(2) - b^(2) - 2b -1

Area of the quadrilateral formed with the foci of the hyperbola x^2/a^2-y^2/b^2=1 and x^2/a^2-y^2/b^2=-1 (a) 4(a^2+b^2) (b) 2(a^2+b^2) (c) (a^2+b^2) (d) 1/2(a^2+b^2)

If the equation of the locus of a point equidistant from the points (a_1, b_1) and (a_2, b_2) is (a_1-a_2)x+(b_1-b_2)y+c=0 , then the value of c is a a2-a2 2+b1 2-b2 2 sqrt(a1 2+b1 2-a2 2-b2 2) 1/2(a1 2+a2 2+b1 2+b2 2) 1/2(a2 2+b2 2-a1 2-b1 2)

RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. Prove that: |(b+c)^2a^2a^2b^2(c+a)^2b^2c^2c^2(a+b)^2|=2a b c(a+b+c)^3

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  2. Show that: |(b+c)^2b a c a a b(c+a)^2c b a c b c(a+b)^2|=2a b c(a+b+c)...

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  3. Show that: |1+a^2-b^2 2a b-2b2a b1-a^2+b^2 2a2b-2a1-a^2-b^2|=(1+a^2+b^...

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  4. Show that: |b^2+c^2a b a c b a c^2+a^2b cc a c b a^2+b^2|=4a^2\ b^2\ c...

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  5. Prove that: |a b a x+b y b c b x+c y a x+b y b x+c y0|=(b^2-a c)(a x^2...

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  6. Without expanding the determinant, show that (a+b+c) is a factor of ...

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  7. If a ,\ b ,\ c are roots of the equation x^3+p x+q=0 , prove that d...

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  8. Find dy/dx if y=cos^2x

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  9. If a+b+c!=0 and , \begin{vmatrix} a & b & c \\ b & c & a \\ ...

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  10. If a , b , c are real numbers, prove that \begin{vmatrix} a & b & ...

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  11. Show that: |a b-cc+b a+c b c-a a-bb+a c|=(a+b+c)(a^2+b^2+c^2)dot

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  12. Using properties of determinants. Prove that |[3a,-a+b,-a+c], [-b+a,3b...

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  13. Using properties of determinants, solve for x:|[a+x, a-x, a-x], [a-x...

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  14. Using properties of determinants, solve the following for x: |[x-2,...

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  15. If a,b,c are all distinct and |[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^3,c^4-...

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  16. If a , b , c are all positive and are p t h ,q th and r t h terms of a...

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  17. If x+y+z=0 prove that | xa yb zc yc za xb zb xc ya y|=x y z|a b c...

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  18. Prove that: |[b, c-a^2,c] ,[a-b^2,a b-c^2,c ],[a-b^2,a ,b-c^2b c-a^2a ...

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  19. Prove that: |[bc-a^2, ca-b^2,ab-c^2],[ca-b^2,ab-c^2,bc-a^2],[ab-c^2,bc...

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  20. Find a quadratic polynomial varphi(x) whose zeros are the maximum ...

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