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By using properties of determinants. Show that:`|1xx^2x^2 1xxx^2 1|=(1-x^3)^2`

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By using properties of determinants.Show that: det[[1,x,x^(2)x^(2),1,xx,x^(2),1]]=(1-x^(3))^(2)

By using properties of determinants. Show that: |1+a^2-b^2 2a b-2b2a b1-a^2+b^2 2a2b-2a1-a^2-b^2|=(1+a^2+b^2)^3

If x,y,z are different and Delta=det[[x,x^(2),x^(3)-1y,y^(2),y^(3)-1z,z^(2),z^(3)-1]]=0, then using properties of determinants,show that xyz=1

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Using properties of determinants.Prove that |xx^(2)1+px^(3)yy^(2)1+py^(3)zz^(2)1+pz^(3)|=(1+pxyz)(x-y)(y-z)(z-x) where p is any scalar.

By using properties of determinants.Show that: det[[a^(2)+1,ab,acab,b^(2)+1,bcca,cb,c^(2)+1]]=(1+a^(2)+b^(2)+b^(2))

Using properties of determinant prove that: |[1,x+y, x^2+y^2],[1, y+z, y^2+z^2],[1, z+x, z^2+x^2]|= (x-y)(y-z)(z-x)

Using properties of determinants, prove the following: |[1,x,x^2],[x^2, 1,x],[x,x^2,1]|=(1-x^3)^2

Using properties of determinants, prove the following: |[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)

MODERN PUBLICATION-DETERMINANTS-NCERT FILE (Exercise 4.2)
  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. Use the properties of determinant and without expanding prove that |...

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  6. By using properties of determinants in |{:(0,a,-b),(-a,0,-c),(b,c,0):}...

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  7. Using properties of determinants, prove that |-a^2a b a c b a-b^2b cc...

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  8. Prove that |(1,a,a^2),(1,b,b^2),(1,c,c^2)|=(a-b)(b-c)(c-a)

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  9. Prove that: (i) |{:(,1,1,1),(,a,b,c),(,a^(3),b^(3),c^(3)):}|=(a-b)(b...

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  10. [[x, x^2, yz],[y, y^2, zx],[z, z^2, xy]]=(x-y)(y-z)(z-x)(xy+yz+zx)

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  11. By using properties of determinants. Show that: (i) |x+4 2x2x2xx+4 2x2...

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  12. Prove, using properties of determinants: |y+k y y y y+k y y y y+k|=k^...

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  13. Prove 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. Prove that Det[[x+y+2z,x,y],[z,y+z+2x,y],[z,x,z+x+2y]]=2(x+y+z)^3

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  15. By using properties of determinants. Show that:|1xx^2x^2 1xxx^2 1|=(1-...

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

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  17. Using properties of determinants, prove the following: |a^2a b a c...

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  18. Let A be a square matrix of order 3xx3, then |k A|is equal to(A) k|A|...

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  19. Which of the following is correct ?

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