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Using properties of determinants prove t...

Using properties of determinants prove that
`|{:(a^2+2a,2a+1,1),(2a+1,a+2,1),(3,3,1):}|=(a-1)^3`

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Answer any three questions Using properties of determinants, prove the following abs{:(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.

Without expanding the determinants 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 the properties of determinants, show that abs[[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

Evalute the determinant |(-2,2,1),(1,4,2),(-2,-3,1)|

Evaluate the following determinants |{:(1,1,1),(2,2,2),(3,3,3):}|

ARIHANT PUBLICATION-DETERMINANTS -PART -1 QUESTION FOR PRACTICE
  1. Prove that |(1, a, a^3),(1, b, b^3),(1, c, c^3)|= (a-b)(b-c)(c-a)(a+b+...

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  2. using the properties of determinants prove that |{:(1,x+y,x^2+y^2),(...

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  3. Using properties of determinants prove that |{:(a^2+2a,2a+1,1),(2a+1...

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  4. Prove that the following. [[(a+1)(a+2),a+2,1],[(a+2)(a+3),a+3,1],[(a+3...

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  5. Using properties of determinants solve the following for x, |{:(x+a,x,...

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  6. Solve [[a+x,a-x,a-x],[a-x,a+x,a-x],[a-x,a-x,a+x]]=0

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  7. IF |{:(4-x,4+x,4+x),(4+x,4-x,4+x),(4+x,4+x,4-x):}|=0 then find the val...

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  8. Prove the following : [[1,x,x^2],[x^2,1,x],[x,x^2,1]]=(1-x^3)^2

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  9. Using properties of determinant prove that |{:(alpha,beta,gamma),(alph...

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  10. IF a,b and c are real numbers and Delta=|{:(b+c,c+a,a+b),(c+a,a+b,b+c)...

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  11. Using the properties of determinants prove that |{:(a+b+2c,a,b),(c,b...

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  12. Find the value of x if |(2x,3),(1,x)|=|(3,4),(-1,2)|

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  13. Prove that |[x+y, x, x],[5x+4y, 4x, 2x], [10x+8y, 8x, 3x]|=x^3

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  14. If x,y and z are different and Delta=|{:(x,x^2,1+x^3),(y,y^2,1+y^3),...

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  15. Prove that abs[[b+c,c+a,a+b],[q+r,r+p,p+q],[y+z,z+x,x+y]]=2abs[[a,b,c]...

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  16. Show that Delta =Delta1 where Delta=|{:(Ax,x^2,1),(By,y^2,1),(Cz,z^2...

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  17. IFDelta=|{:(1,x,x^2),(1,y,y^2),(1,z,z^2):}| and Delta1=|{:(1,1,1),(yz,...

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  18. Using properties of determinants, prove that |{:(y^2z^2,yz,y+z),(z^2x^...

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  19. If f(x)=|{:(a,-1,0),(ax,a,-1),(ax^2,ax,a):}| then using properties of...

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  20. Find the maximum value of Delta=|{:(1,1,1),(1,1+sin theta,1),(1,1,1+co...

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