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Write the value of Delta=|{:(x+y,y+z,z+x...

Write the value of `Delta=|{:(x+y,y+z,z+x),(z,x,y),(-3,-3,-3):}|`

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If x,y and z are different and Delta=|{:(x,x^2,1+x^3),(y,y^2,1+y^3),(z,z^2,1+z^3):}|=0 then show that 1+xyz=0

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Find the value of x,y, and z if A=[[0,2y,z],[x,y,-z],[x,-y,z]] satisfies A^1=A^(-1) .

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Write the value of x-y+z from the relation [[x+y+z],[x+z],[y+z]]=[[4],[8],[5]] .

using the properties of determinants prove that |{:(1,x+y,x^2+y^2),(1,y+z,y^2+z^2),(1,z+x,z^2+x^2):}|=(x-y)(y-z)(z-x)

ARIHANT PUBLICATION-DETERMINANTS -PART -1 QUESTION FOR PRACTICE
  1. IF A is 3 times 3 matrix |A| ne 0 and |3A|=k|A| then find the value of...

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  2. Without expanding,show that the following determinant vanishes. abs ((...

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  3. Write the value of Delta=|{:(x+y,y+z,z+x),(z,x,y),(-3,-3,-3):}|

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  4. Show that |{:(a,b,c),(a+2x,b+2y,c+2z),(x,y,z):}|=0

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  5. Write the value of |[2,7,65],[3,8,75],[5,9,86]|

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  6. Find the value of |{:(17,58,97),(19,60,99),(18,59,98):}| without expan...

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  7. Solve for x, |{:(15-2x,11,10),(11-3x,17,16),(7-x,14,13):}|=0

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  8. IF cos 2 theta=0 then simplify |{:(0,cos theta, sin theta),(cos theta,...

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

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

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

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

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

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

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

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

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

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