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Using the property of determinants and w...

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: |[1,bc,a(b+c)],[1,ca,b(c+a)],[1,ab,c(a+b]| = 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)|

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

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)

Using properties of determinants, prove that: |[x,x^2,1+px^3],[y,y^2,1+py^3],[z,z^2,1+pz^3]| = (1+pxyz)(x-y)(y-z)(z-x)

BETTER CHOICE PUBLICATION-DETERMINANTS -ASSIGNMENT (MOST IMPORTANT QUESTIONS FOR PRACTICE) (SECTION III)
  1. Without expanding show that the following determinants vanish |(42,...

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

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  3. Without expanding show that the following determinants vanish |(4,a...

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  4. Without expanding show that the following determinants vanish |(3,1...

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  5. Prove that |[1,a,a^2-bc],[1,b,b^2-ca],[1,c,c^2-ab]|= 0

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

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  7. The value of the det. |[2,a,abc],[2,b,bca],[2,c,cab]| is

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

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  9. Prove that: |[x+y,x,x],[5x+4y,4x,2x],[10x+8y,8x,3x]|=x^3.

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

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

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  12. Prove that |[b+c,a,a],[b,c+a,b],[c,c,a+b]| = 4abc

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

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  14. Without expanding, prove the following |(0,ab^2,ac^2),(a^2b,0,bc^2)...

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  15. Without expanding, prove the following |(y+z,z,y),(z,z+x,x),(y,x,x+...

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  16. Without expanding, prove the following |(a,a+b,a+2b),(a+2b,a,a+b),(...

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  17. Prove that: |[1,1+p,1+p+q],[2,3+2p,4+3p+2q],[3,6+3p,10+6p+3q]|=1

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  18. Without expanding, prove the following |(1+a^2-b^2,2ab,-2b),(2ab,1-...

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  19. Without expanding, prove the following |(x,x+y,x+2y),(x+2y,x,x+y),(...

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  20. Show that: |[x-y-z,2x,2x],[2y,y-z-x,2y],[2z,2z,z-x-y]|=(x+y+z)^3

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