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Using the property of determinants and w...

Using the property of determinants and without expanding , prove that: `|[2,7,65],[3,8,75],[5,9,86]| = 0`

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

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

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

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]|

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)|

Without expanding, prove that |(6,2,3),(9,3,5),(12,4,7) = 0

Without expanding, prove that the following determinant vanishes. |(2,7,65),(3,8,75),(5,9,86)|

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PSEB-DETERMINANTS-Exercise
  1. Using the property of determinants and without expanding , prove that:...

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

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

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

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  7. Prove that: |[-a^2, ab,ac],[ba,-b^2,bc],[ca,cb,-c^2]|=4a^2b^2c^2

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

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  10. By using properties of determinants, show that : |[x+4,2x,2x],[2x,x+4...

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  11. Prove that: |[x,x^2,yz],[y,y^2,zx],[z,z^2,xy]|=(x-y)(y-z)(z-x)(xy+yz+z...

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  12. Prove that : |[y+k,y,y],[y,y+k,y],[y,y,y+k]|=k^2(3y+k).

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  13. Show that: |[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]|=(a+b+c)^3

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  14. By using properties of determinants, show that : |[x+y+2z,x,y],[z,y+...

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  15. By using properties of determinants, show that : |[1,x,x^2],[x^2,1,x...

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  16. Using the properties of determinant, show that :|[a^2+1,ab,ac],[ab,b^2...

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  17. Let A be a square matrix of order 3 xx 3. Then I kA I is equal to :

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  18. Which of the following is correct

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  19. Find area of the triangle with vertices at the point given in the fol...

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  20. Find area of the triangle with vertices at the point given in the fol...

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