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Using properties of determinants show ...

Using properties of determinants show
that
`abs[[1+a,1,1],[1,1+b,1],[1,1,1+c]]=abc(1+1/a+1/b+1/c)`

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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) .

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The value of the determinant abs[[1,1,1],[1,-1,-1],[1,1,-1]] is

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Show that abs[[1,a,a^2],[1,b,b^2],[1,c,c^2]]=(a-b)(b-c)(c-a)

By using the properties of determinants,prove that |[a^2+1,ab ,ac],[ab,b^2+1,bc],[ca ,cb,c^2+1]|=1+a^2+b^2+c^2

By using the properties of determinants,prove that |[1+a^2-b^2,2ab ,-2b],[2ab,1-a^2+b^2,2a],[2b ,-2a,1-a^2-b^2]|=(1+a^2+b^2)^3

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BODY BOOKS PUBLICATION-DETERMINANTS-EXERCISE
  1. If [[2,5],[-3,7]]xxA=[[17,-1],[47,-13]] then Find the 2x2 matrix A.

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  2. If [[2,5],[-3,7]]xxA=[[17,-1],[47,-13]] then Find A^2.

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  3. Using properties of determinants show that abs[[1+a,1,1],[1,1+b,1]...

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  4. Consider the point A(-2,-3),B(3,2),C(-1,-8) Find the area of Delt...

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  5. Consider the point A(-2,-3),B(3,2),C(-1,-8) Find third vertex of any...

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  6. If A=[(2,-3),(4,6)].Find adj A.

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  7. If A=[(2,-3),(4,6)]. Find A^-1.

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  8. Given Delta=|(y+z,x,y),(z+x,z,x),(x+y,y,z)| Apply R1rarrR1+R2+R3.

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  9. Given Delta=|(y+z,x,y),(z+x,z,x),(x+y,y,z)| Take (x+y+z) common from R...

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  10. Given Delta=|(y+z,x,y),(z+x,z,x),(x+y,y,z)| Perform C1rarrC1-2C3,C2rar...

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  11. Given Delta=|(y+z,x,y),(z+x,z,x),(x+y,y,z)| Prove that Delta=(x+y+z)(x...

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  12. Let A=[(-1,2,4),(1,1,3),(3,2,3)] Find |A|.

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  13. Let A=[(-1,2,4),(1,1,3),(3,2,3)] Find Adj A.

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  14. Let A=[(-1,2,4),(1,1,3),(3,2,3)] Verify that A. AdjA=|A|.I

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  15. Consider A=[(4,1),(5,3)]. Find A^-1 and A^T

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  16. Consider A=[(4,1),(5,3)]. Verify (A^T)^-1=(A^-1)^T.

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  17. Let A=[(1,4,0),(-1,2,2),(0,0,2)] Is A singular?

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  18. Let A=[(1,4,0),(-1,2,2),(0,0,2)] Find Adj A.

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  19. Let A=[(1,4,0),(-1,2,2),(0,0,2)] Find A^-1

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  20. Evaluate |[x, y, x+y],[ y, x+y, x],[ x+y, x, y]|

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