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Using properties of determinants, prove the following: `|a^2a b a c a bb^2+1b cc a c b c^2+1|=1+a^2+b^2+c^2dot`

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Prove: |a^2+1a b a c a bb^2+1b cc a c b c^2+1|=1+a^2+b^2+c^2

Using properties of determinants,prove the following: det[[a^(2),ab,acab,b^(2)+1,bcca,cb,c^(2)+1]]=1+a^(2)+b^(2)+c^(2)

Using properties of determinants,prove the following det[[a^(2),ab,acab,b^(2)+1,bcca,cb,c^(2)+1]]=1+a^(2)+b^(2)+c^(2)

Using properties of determinants, prove that |[a^2, bc, ac+c^2] , [a^2+ab, b^2, ac] , [ab, b^2+bc, c^2]| = 4a^2b^2c^2

Using properties of determinants, prove that following |(a+b+2c,a,b),(c,b+c+2a,b),(c,a,c+a+2b)|=2(a+b+c)^3

Using properties of determinants, prove that: |[b^2+c^2,a^2,a^2],[b^2,c^2+a^2,b^2],[c^2,c^2,a^2+b^2]|=4a^2b^2c^2

Using properties of determinants,prove that det[[-a^(2),ab,acba,-b^(2),bcca,cb,-c^(2)]]=4a^(2)b^(2)c^(2)

Using properties of determinants,prove the following : det[[a,a^(2),bcb,b^(2),cac,c^(2),ab]]=(a-b)(b-c)(c-a)(bc+ca+ab)

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 |a+b+c-c-b-c a+b+c-a-b-a a+b+c|=2(a+b)(b+c)(c+a)

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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