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Using the property of determinants and w...

Using the property of determinants and without expanding , prove that:`|[b+c,q+r,y+z)],[c+a,r+p,z+x],[a+b,p+q,x+y]| = 2|[a,p,x],[b,q,y],[c,r,z]|`

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Using the property of determinants and without expanding prove that : {:|(b+c,q+r,y+z),(c+a,r+p,z+x),(a+b,p+q,x+y)|=2|(a,p,x),(b,q,x),(c,r,z)|

Using the property of determinants and without expanding , prove that: |[x,a,x+a],[y,b,y+b],[z,c,z+c]| = 0

Using the properties of determinants, show that : |[[x, y, z],[x^2, y^2, z^2],[x,y,z]]|= 0 .

Using the properties of determinants, prove that : |[[a+x,y,z],[x,a+y,z],[x,y,a+z]]|=a^2(a+x+y+z)

Without expanding prove that |(a,b,c),(x,y,z),(p,q,r)| = |(y,b,q),(x,a,p),(z,c,r)|

Without expanding , show that |(a,b,c),(a+2x,b+2y,c+2z),(x,y,z)|= 0 .

Without expanding, prove that Delta = abs{:(x+y, y + z, z+ x),(z, x , y),(1,1,1):} = 0

Using properties of determinants, prove that |b+c q+r y+z c+a r+p z+x c+b p+q x+y|=2\ |a p x b q y c r z|

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MODERN PUBLICATION-DETERMINANTS-EXERCISE
  1. Evaluate |[x,y,x+y],[y,x+y,x],[x+y,x,y]|

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  2. Evaluate |[1,x,y],[1,x+y,y],[1,x,x+y]|

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  3. Using the property of determinants and without expanding , prove that:...

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  4. Using the property of determinants and without expanding , prove that:...

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  5. Without expanding, prove the following |(x+4,x,x),(x,x+4,x),(x,x,x+...

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  6. using properties of determinant, prove that abs{:(y+k , y , y ),(y , y...

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  7. Prove that: {:|(x,y,x+y),(y,x+y,x),(x+y,x,y)| = -2(x^3+y^3)

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  8. By using properties of determinants, show that : |[1,a,a^2],[1,b,b^2]...

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  9. Prove that: {:|(a,b-c,c+b),(a+c,b,c-a),(a-b,b+a,)|=(a+b)+c)(a^2+b^2+...

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  10. Prove that: {:|(1,a,a),(a,1,a),(a,a,1)|= (2a+1),(1-a)^2

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

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  12. Prove that: {:|(1,1,1),(a,b,c),(bc,ca,ab)| = (a-b)(b-c)(c-a)

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  13. Prove that: {:|(1,a,bc),(1,b,ca),(1,c,ab)|=(a-b)(b-c)(c-a)

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  14. Prove that: {:|(bc,a,1),(ca,b,1),(ab,c,1)| = (a-b)(b-c)(a-c)

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  15. Without expanding, prove the following |(a,b,c),(a^2,b^2,c^2),(bc,c...

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  16. Prove that: {:|(a^2,a,b+c),(b^2,b,c+a),(c^2,c,ab)| = -(a+b+c)(a-b)(b...

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  17. Prove that: {:|(b+c,a-b,a),(c+a,b-c,b),(a+b,c-a,c)|=3abc -a^3-b^3-c^...

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  18. Prove that |{:(b^(2)+c^(2),ab,ac),(ab,c^(2)+a^(2),bc),(ac,bc,a^(2)+b...

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  19. Prove that: {:|(1+a^2-b^2,2ab,-2b),(2ab,1-a^2+b^2,2a),(2b,-2a,1-a^2-...

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  20. Prove that: {:|(x,y,z),(x^2,y^2,z^2),(x^3,y^3,z^3)|=|(x,x^2,x^3),(y,...

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