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

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

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Without expanding show that |{:(x,a,x+a),(y,b,y+b),(z,c,z+c):}|=0

Without expanding , show that |{:(x,a,x+a),(y,b,y+b),(z,c,z+a):}|=0

Using properties of determinants prove that |{:(a+x,y,z),(x,a+y,z),(x,y,a+z):}|=a^2 (a+x+y+z)

Prove that |{:(x,y,z),(x^2,y^2,z^2),(yz,zx,xy):}|=|{:(1,1,1),(x^2,y^2,z^2),(x^3,y^3,z^3):}|=(x-y) (y-z) (z-x) (xy+yz+zx)

Show that |{:(1,x, x ^(3)),(1,y,y ^(3)),(1,z,z^(3)):}| = (x-y) (y-z) (z-x) (x + y + z)

Using the properties of determinants prove that |{:(a+b+2c,a,b),(c,b+c+2a,b),(c,a,c+a+2b):}|=2(a+b+c)^3 or |{:(x+y+2z,x,y),(z,y+z+2x,y),(z,x,z+x+2y):}|=2(x+y+z)^3

Using properties of determinants, prove that |{:(y^2z^2,yz,y+z),(z^2x^2,zx,z+x),(x^2y^2,xy,x+y):}|=0

ARIHANT PUBLICATION-DETERMINANTS -PART -1 QUESTION FOR PRACTICE
  1. Without expanding,show that the following determinant vanishes. abs ((...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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