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Without expanding,show that the followin...

Without expanding,show that the following determinant vanishes. `abs ((1,bc,a(b+c)),(1,ca,b(c+a)),(1,ab,c(a+b)))`

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ARIHANT PUBLICATION-DETERMINANTS -PART -1 QUESTION FOR PRACTICE
  1. Let A be a square matrix of order 3 times 3 Write the value of |2A| wh...

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  2. IF A is 3 times 3 matrix |A| ne 0 and |3A|=k|A| then find the value of...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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