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Using the property of determinants and w...

Using the property of determinants and without expanding prove the following
`|{:(1,a,b+c),(1,b,c+a),(1,c,a+b):}|=0`

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Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(1,1,1),(a,b,c),(a^3,b^3,c^3):}|=(a-b)(b-c)(c-a)(a+b+c)

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Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(1,bc,a(b+c)),(1,ca,b(c+a)),(1,ab,c(a+b)):}|=0

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(0,a,-b),(-a,0,-c),(b,c,0):}|=0

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(a-b,b-c,c-a),(b-c,c-a,a-b),(c-a,a-b,b-c):}|=0

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(x,a,x+a),(y,b,y+b),(z,c,z+c):}|=0

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b):}|=(a+b+c)^3

KUMAR PRAKASHAN-DETERMINANTS -Practice Work
  1. If |{:(x,1,2),(1,0,3),(5,-1,4):}|=0 then find x

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  2. Using the property of determinants and without expanding prove the fol...

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  3. Using the property of determinants and without expanding prove the fol...

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  4. Using the property of determinants and without expanding prove the fol...

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  5. Using the property of determinants and without expanding prove the fol...

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  6. Using the property of determinants and without expanding prove the fol...

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  7. Using the properties of determinants, solve the following for x |{:(...

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  8. Prove that |{:(a+1,1,1),(1,b+1,1),(1,1,c+1):}|=abc(1/a+1/b+1/c+1)

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  9. Using the properties of determinants, prove the following |{:((b+c)^...

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  10. Using the properties of determinants, prove the following |{:((x-2)^...

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  11. Using the properties of determinants, prove the following It 2s=a+b+...

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  12. Using the properties of determinants, prove the following |{:(a^2,b^...

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  13. If p^(th),q^(th)and r^(th) tern of G.P are a,b and c respectively then...

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  14. If a,b,c are A.P then |{:(x+1,x+2,x+a),(x+2,x+3,x+b),(x+3,x+4,x+c):}...

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  15. Using the properties of determinants, prove the following |{:(a,b-c,...

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  16. Using the properties of determinants, prove the following |{:((a+b)^...

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  17. Find area of the triangle withh vertices at the point given in each of...

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  18. Find area of the triangle withh vertices at the point given in each of...

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  19. Find area of the triangle withh vertices at the point given in each of...

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  20. Find area of the triangle with vertices at the point given in each of ...

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