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Using properties of determinants prove ...

Using properties of determinants prove the
following.
`abs[[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=(a+b+c)^3`

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Without expanding the determinant prove the following. |[a-b,b-c,c-a],[b-c,c-a,a-b],[c-a,a-b,b-c]|=0

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BODY BOOKS PUBLICATION-DETERMINANTS-EXERCISE
  1. If Delta=[(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)] Perform R1rarrR1+...

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  2. If Delta=[(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)]Perform R1rarrR1+R...

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  3. Using properties of determinants prove the following. abs[[a-b-c,...

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  4. Given Delta=[(a+b,b+c,c+a),(b+c,c+a,a+b),(c+a,a+b,b+c)] Express given ...

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  5. Show that abs[[a+b,b+c,c+a],[b+c,c+a,a+b],[c+a,a+b,b+c]]=2abs[[a,b,c],...

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  6. Find the equation of line joining (1,2) and (3,6) using determinants.

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  7. Prove that |[x,sintheta, costheta],[-sintheta,-x,1],[costheta,1,x]| is...

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  8. Prove that |[x,sintheta, costheta],[-sintheta,-x,1],[costheta,1,x]| is...

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  9. using properties of determinants, prove that abs[[1,a,a^2],[1,b,b^2],...

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  10. If A=[[2,-3,5],[3,2,-4],[1,1,-2]] Find A^-1

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  11. If A=[[2,-3,5],[3,2,-4],[1,1,-2]] Using it solve the system of equat...

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  12. prove that abs[[a,b,c],[a+2x,b+2y,c+2z],[x,y,z]]=0

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  13. if A=[[1,-1,2],[0,2,-3],[3,-2,4]] B=[[-2,0,1],[9,2,-3],[6,1,-2]] Prov...

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  14. if A=[[1,-1,2],[0,2,-3],[3,-2,4]] B=[[-2,0,1],[9,2,-3],[6,1,-2]] ...

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  15. If A=[[a,1],[1,0]] is such that A^2=I then a equals

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  16. Solve the system of equations x-y+z=4,2x+y-3z=0,x+y+z=2 Using matr...

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  17. The value of abs((x,x-1) , (x+1,x):} is a)1 b)x c)x^2d)0

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  18. Using properties of determinants prove the following. abs[[1,x,x^2...

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  19. Prove that |(1,x,x^3),(1,y,y^3),(1,z,z^3)|=(x+y+z)(x-y)(y-z)(z-y).

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  20. Prove that abs[[1!,2!,3!],[2!,3!,4!],[3!,4!,5!]]=4!

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