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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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Prove that abs[[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=(a+b+c)^3

Using properties of determinants prove the following. abs[[b+c,a,a],[b,c+a,b],[c,c,a+b]]=4abc

Using properties of determinants prove the following. abs[[1,a,bc],[1,b,ca],[1,c,ab]]=(a-b)(b-c)(c-a)

Using properties of determinants prove the following. abs[[1,1,1],[a,b,c],[a^3,b^3,c^3]]=(a-b)(b-c)(c-a)(a+b+c)

using properties of determinants, prove that abs[[1,a,a^2],[1,b,b^2],[1,c,c^2]]=(a-b)(b-c)(c-a) .

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

By using properties of determinants, prove that |[0,a ,-b],[-a,0,-c],[b,c,0]|=0

Using properties of determinants, show that abs[[a,a^2,b+c],[b,b^2,c+a],[c,c^2,a+b]]=(b-c)(c-a)(a-b)(a+b+c)

By using properties of determinants, prove that |[-a^2,ab,ac],[ba,-b^2,bc],[ca,cb,-c^2]|=4a^2b^2c^2

Using properties of determinants, prove that |[3a,-a+b,-a+c],[-b+a,3b,-b+c],[-c+a,-c+b,3c]| = 3(a+b+c)(ab+bc+ca)

MAXIMUM PUBLICATION-DETERMINANTS-EXAMPLE
  1. A=[[1,-3,1],[2,0,4],[1,2,-2]] Show that AxxadjA=abs[A]I

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  2. A=[[1,-3,1],[2,0,4],[1,2,-2]] Find abs[3A]

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

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  4. Using properties of determinants prove the following. abs[[b+c,a,...

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  5. Ifabs[[1,-3,2],[4,-1,2],[3,5,2]]=40,thenabs[[1,4,3],[-3,-1,5],[2,2,2]]...

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  6. Calculate abs[[3,-3,2],[12,-1,2],[9,5,2]]=

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  7. Show that Delta=abs[[-a^2,ab,ac],[ba,-b^2,bc],[ac,bc,-c^2]]=4a^2b^2c^2

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  8. Find x if abs[[2,4],[5,1]]=abs[[2x,4],[6,x]]

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  9. S.Tabs[[x+a,b,c],[a,x+b,c],[a,b,x+c]]=x^2(x+a+b+c)

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  10. Prove that abs[[(b+c)^2,a^2,a^2],[b^2,(c+a)^2,b^2],[c^2,c^2,(a+b)^2]] ...

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  11. Let the value of a determinant is Delta. Then the value of a determi...

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  12. 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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  13. Test the consistency 3x-y-2z=2,2y-z=-1,3x-5y=3

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  14. Consider the system of equations 2x-3y=7 and 3x+4y=5 Express the s...

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  15. Consider the system of equations 2x-3y=7 and 3x+4y=5 Find adjA

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  16. Consider the system of equations 2x-3y=7 and 3x+4y=5 Solve the sys...

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  17. If A and B are matrices of order 3 such that abs[A]=-1,abs[B]=3,then...

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  18. If A=[[1,tanx],[-tanx,1]],Show that A^TA^(-1)=[[cos2x,-sin2x],[sin2x...

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  19. Consider the determinant Delta=abs[[x,x^2,1+x^3],[y,y^2,1+y^3],[z,z^2,...

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  20. Consider the determinant Delta=abs[[x,x^2,1+x^3],[y,y^2,1+y^3],[z,z^2,...

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