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|[1+a^2-b^2,2ab,-2b],[2ab,1-a^2+b^2,2a],...

`|[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,-2b2ab,1-a^(2)+b^(2),2a2b,-2a,1-a^(2)-b^(2)]|=(1+a^(2)+b^(2))^(3)

Let ab=1,Delta=|{:(1+a^2-b^2, 2ab,-2b),(2ab,1-a^2+b^2, 2a),(2b,-2a,1-a^2-b^2):}| then the minimum value of Delta is :

Let ab=1,Delta=|{:(1+a^2-b^2, 2ab,-2b),(2ab,1-a^2+b^2, 2a),(2b,-2a,1-a^2-b^2):}| then the minimum value of Delta is :

Find the value |{:(1+a^(2)-b^(2),2ab,-2b),(2ab,1-a^(2)+b^(2),2a),(2b,-2a,1-a^(2)-b^(2)):}|

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

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

(a^2+b^2+2ab)-(a^2+b^2-2ab)

|[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)]|

a^3 - b^3 - 3a^2b+ 3ab^2, by, a^2 + b^2 - 2ab

prove that |[a,b,0],[0,a,b],[b,0,a]|=a^3+b^3,hence find the value of |[2ab,a^2,b^2],[a^2,b^2,2ab],[b^2,2ab,a^2]|

MODERN PUBLICATION-DETERMINANTS-Exercise 4(b) (LONG ANSWER TYPE QUESTIONS (II))
  1. Evaluate the following: |[a^2+2a, 2a+1, 1],[2a+1, a+2, 1],[3,3,1]|

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  2. Given : a^(2)+b^(2)+c^(2) =0 Prove the following : |{:(b^(2)+c^(2...

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  3. |[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...

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  4. Prove the following : |{:(x,y,z),(x^(2),y^(2),z^(2)),(x^(3),y^(3),z^...

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  5. [[x, x^2, yz],[y, y^2, zx],[z, z^2, xy]]=(x-y)(y-z)(z-x)(xy+yz+zx)

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  6. Prove that : |{:(x+y+2z,x,y),(z,y+z+2x,y),(z,x,x+a+2y):}|=2(x+y+)^(3)

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  7. Prove that |{:(b+c, c+a, a+b),(c+a, a+b,b+c),(a+b, b+c, c+a):}| =2(...

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  8. Using properties of determinants, prove the following: |xx+y x+2y\...

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  9. |[b+c, a,a] , [b,c+a,b] , [c,c,a+b]|=4abc

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  10. Prove the following : |{:(2ab,a^(2),b^(2)),(a^(2),b^(2),2ab),(b^(2),...

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  11. Prove the following : |(1,x,x^(2)-yz),(1,y,y^(2)-zx),(1,z,z^(2)-xy)|=...

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  12. For any scalar p prove that =|xx^2 1+p x^3y y^2 1+p y^3z z^2 1+p z^3|=...

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  13. |(x+y+z,-z,-y),(-z,x+y+z,-x),(-y,-x,x+y+z)|=2(x+y)(y+z)(z+x)

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  14. Prove: |2y y-z-x2y2z2z z-x-y x-y-z2x2x|=(x+y+z)^3

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  15. |(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)|

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  16. Show that: |3a-a+b-a+c-b+a3b-b+c-c+a-c+b3c|=3(a+b+c)(a b+b c+c a)dot

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  17. Using properties of determinants. Find the value of 'x' |(4-x,4+x,4+...

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  18. Solve: |a+x a-x a-x a-x a+x a-x a-x a-x a+x|=0

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  19. Prove that |[x, sintheta, costheta],[-sintheta, -x, 1],[costheta, 1, ...

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  20. Prove that |{:(1+a,1,1),(1,1+b,1),(1,1,1+c):}| =abc (1+(1)/(a)+(1)/...

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