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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]|

MOTION-DETERMINANTS -EXERCISE-3
  1. Without expanding as far as possible, prove that |{:(1,1,1),(x,y,z),...

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

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

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  5. Show that the value of the determinant |(tan(A+Q),tan(B+P),tan(C+P)),...

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  6. Prove that |((beta+gamma-alpha-delta)^4,(beta+gamma-alpha-delta)^2,1),...

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  7. Solve for x, |[x+2,2x+3,3x+4] , [2x+3,3x+4,4x+5] , [3x+5,5x+8, 10x+17]...

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  8. Solve : |x-2 2x-3 3x-4x-4 2x-9 3x-16 x-8 2x-27 3x-64|=0

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  9. If a + b + c = 0 one root of |(a -x,c,b),(b,b -x,a),(b,a,c -x)|= 0, is

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  10. If a^2+b^2+c^2=1 then show that value of the determinant |a^2+(b^2+c^2...

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  11. 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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  12. Show that | [a^2 +lambda, ab, ac], [ab, b^2+lambda, bc], [ac, bc, c^2+...

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  13. Prove that :|[a^2,b^2,c^2], [(a+1)^2, (b+1)^2, (c+1)^2], [(a-1)^2, (b-...

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  14. In triangle A B C , if |1 1 1cotA/2cotB/2cotC/2tanB/2+tanC/2tanB/2+tan...

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  15. Prove that |{:(2,alpha+beta+gamma+delta,alphabeta +gammadelta),(alph...

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  16. Solve for x the equation |(a^(2),a,1),(sin(n+1)x,sin nx,sin(n-1)x),(...

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  17. Solve the following sets of equations using Cramer's rule and remark a...

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  18. Solve the following sets of equation using Cramers rule and remark a...

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  19. Solve the following sets of equation using Cramers rule and remark a...

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  20. For what value of K do the following system of equations poss...

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