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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|

Using the properties of determinants show that : |[[p^2, q^2, r^2],[qr,rp,pq],[p,q,r]]|=(p-q)(q-r)(r-p)(pq+qr+rp)

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

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

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

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

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

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

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

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

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

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  16. Which of the following is correct

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

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

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

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  20. Show that points A(a,b+c),B(b,c+a) ਅਤੇ C(c,a+b) are collinear.

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