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Show that |[b^2+c^2,ab,ac],[ba,c^2+a^2,b...

Show that `|[b^2+c^2,ab,ac],[ba,c^2+a^2,bc],[ca,cb,a^2+b^2]|=4a^2b^2c^2`

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Prove the identity: |[b^2+c^2,ab, ac],[ba,c^2+a^2,bc],[ca, cb ,a^2+b^2]|=4a^2b^2c^2

Prove the identities: |[b^2+c^2,ab, ac],[ba,c^2+a^2,bc],[ca, cb ,a^2+b^2]|=4a^2b^2c^2

abs([-a^2,ab,ac],[ba,-b^2,bc],[ca,cb,-c^2]) = 4a^2.b^2.c^2

Show that: |b^2+c^2a b a c b a c^2+a^2b c c a c b a^2+b^2|=4a^2b^2c^2

|[x^2+a^2,ab,ac] , [ab,x^2+b^2,bc] , [ac,bc,x^2+c^2]|=

Prove that |[a^2+1,ab,ac],[ab,b^2+1,bc],[ac,bc,c^2+1]|=1+a^2+b^2+c^2

Using properties of determinants, prove the following: |[a^2 + 1,ab, ac], [ab,b^2 + 1,b c],[ca, cb, c^2+1]|=1+a^2+b^2+c^2

Using properties of determinants, prove that |(-a^2,ab,ac),(ba,-b^2,bc),(ca,cb,-c^2)|=4a^2 b^2 c^2

Show that |[a ,b ,c],[ a^2,b^2,c^2],[bc, ca, ab]|=|[1, 1, 1],[a^2,b^2,c^2],[a^3,b^3,c^3]|=(a-b)(b-c)(c-a)(a b+b c+c a) .

Prove the identities: |{:(b^(2)+c^(2),,ab,,ac),(ab,,c^(2)+a^(2),,bc),(ca,,bc,,a^(2)+b^(2)):}|=4a^2b^2c^2

RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. Prove: |a+b+c-c-b-c a+b+c-a-b-a a+b+c|=2(a+b)(b+c)(c+a)

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  2. Prove: |[b+c,a,a],[b,c+a,b],[c,c,a+b]|=4a b c

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  3. Show that |[b^2+c^2,ab,ac],[ba,c^2+a^2,bc],[ca,cb,a^2+b^2]|=4a^2b^2c^2

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  4. Prove: |(0,b^2a, c^2a),( a^2b,0,c^2b),( a^2c, b^2c,0)|=2a^3b^3c^3

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  5. Prove: |((a^2+b^2)/c,c,c),( a,(b^2+c^2)/a ,a),( b,b,(c^2+a^2)/b)|=4a b...

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  6. Prove: |(-bc, b^2+b c,c^2+bc), (a^2+a c,-a c,c^2+a c),( a^2+a b,b^2+a ...

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

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  8. show that |{:(y+k,y,y),(y,y+k,y),(y,y,y+k):}|=k^(2)(3y+k)

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  9. Prove: |(y+z, z, y),( z, z+x,x),( y, x,x+y)|=4\ x y z

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  10. Show that | (-a(b^2 + c^2 - a^2), 2b^3, 2c^3), (2a^3, -b(c^2 + a...

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  11. Prove: |(1+a,1, 1),( 1, 1+a, 1),(1, 1, 1+a)|=a^3 +3a^2

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  12. Prove: |(2y, y-z-x,2y),(2z,2z, z-x-y),( x-y-z,2x,2x)|=(x+y+z)^3

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  13. show that |[y+z ,x, y],[ z+x, z, x],[x+y, y ,z]|=(x+y+z)(x-z)^2

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  14. Using properties of determinants, prove that |(a+x, y, z),(x, a+y, z)...

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  15. Prove: |a^3 2a b^3 2b c^3 2c|=2(a-b)(b-c)...

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  16. Without expanding, prove that |a b c x y z p q r|=|x y z p q r a b c|=...

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  17. Show that |[x+1,x+2,x+a], [x+2,x+3,x+b],[ x+3,x+4,x+c]|=0 where a ,\ b...

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  18. Show that [[x-3,x-4,x-alpha],[x-2,x-3,x-beta],[x-1,x-2,x-gamma]]=0 whe...

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  19. If a ,\ b ,\ c are real numbers such that |(b+c,c+a ,a+b),( c+a,a+b,...

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  20. a!=p , b!=q,c!=r and |(p,b,c),(a,q,c),(a,b,r)|=0 the value of p/(p-...

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