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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) .

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 the following. abs[[1,a,bc],[1,b,ca],[1,c,ab]]=(a-b)(b-c)(c-a)

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

Show that abs [[1,a,bc],[1,b,ac],[1,c,ab]]=(a-b)(b-c)(c-a)

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

Find the value of the determinant |[1, a, b+c],[ 1, b, c+a],[ 1, c, a+b]|

Evaluate Delta=|[1, a, bc],[ 1, b, c a],[ 1, c, a b]|

A N EXCEL PUBLICATION-DETERMINANTS-QUESTION TYPE
  1. Using properties, prove that |[1,omega,omega^2],[omega,omega^2,1],[om...

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  2. Without expanding the determinant prove the following. |[a-b,b-c,c-a...

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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 determinant D=|[1,3,5],[2,6,10],[31,11,38]| On taking 2 ...

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  5. Consider the determinant D=|[1,3,5],[2,6,10],[31,11,38]| Evaluate De...

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  6. Consider the determinant Delta =|[1,a,a^2-bc],[1,b,b^2-ca],[1,c,c^2-b...

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  7. Consider the determinant Delta =|[1,a,a^2-bc],[1,b,b^2-ca],[1,c,c^2-b...

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  8. Consider the equation |[3x-8,3,3],[3,3x-8,3],[3,3,3x-8]|=0 OperatingC1...

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  9. Consider the equation |[3x-8,3,3],[3,3x-8,3],[3,3,3x-8]|=0 Solve the ...

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  10. Without expanding the determinant prove the following. |[x,a,x+a],[y...

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  11. Without expanding the determinant prove the following. |[2,7,65],[3,...

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  12. Without expanding the determinant prove the following. |[b+c,q+r,y+z...

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  13. Without expanding the determinant prove the following. |[1,bc,a(b+c)...

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  14. Without expanding the determinant prove the following. |[a-b,b-c,c-a...

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

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  16. By using properties of determinants, prove that |[-a^2,ab,ac],[ba,-b^...

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

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  18. Using properties of determinants prove the following. abs[[1,1,1],...

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  19. By using properties of determinants, prove that |[x,x^2,yz],[y,y^2,zx...

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  20. By using properties of determinants, prove that |[x+4,2x,2x],[2x,x+4,...

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