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

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

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|((a^2+b^2)/c,c,c),(a,(b^2+c^2)/a,a),(b,b,(a^2+c^2)/b)| equal to : (A) 4abc (B) a^2+b^2+c^2 (C) (a+b+c)^2 (D) None of These

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

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

Prove: |(a^2,a^2-(b-c)^2,b c), (b^2,b^2-(c-a)^2,c a),( c^2,c^2-(a-b)^2,a b)|=(a-b)(b-c)(c-a)(a+b+c)(a^2+b^2+c^2)

Prove that : |{:(a^(2),b^(2)+c^(2),bc),(b^(2),c^(2)+a^(2),ca),(c^(2),a^(2)+b^(2),ab):}|=-(a-b)(b-c)(c-a)(a+b+c)(a^(2)+b^(2)+c^(2))

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 b,-a b)|=(a b+b c+c a)^3

Prove: |(1,b+c ,b^2+c^2),( 1,c+a ,c^2+a^2),( 1,a+b ,a^2+b^2)|=(a-b)(b-c)(c-a)

Prove that: |[b, c-a^2,c] ,[a-b^2,a b-c^2,c ],[a-b^2,a ,b-c^2b c-a^2a b-c^2b c-a^2c a-b^2]|=|[a, b, c],[ b ,c ,a],[ c, a ,b]|^2 .

Prove: |(a+b,b+c,c+a),( b+c,c+a, a+b),( c+a, a+b,b+c)|=2|(a, b, c),( b, c, a),( c, a, b)|

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

RD SHARMA ENGLISH-DETERMINANTS-All Questions

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: |(0,b^2a, c^2a),( a^2b,0,c^2b),( a^2c, b^2c,0)|=2a^3b^3c^3
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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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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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By using properties of determinants. Show that: (i) |x+4 2x2x2xx+4 2x2...
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show that |{:(y+k,y,y),(y,y+k,y),(y,y,y+k):}|=k^(2)(3y+k)
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Prove: |(y+z, z, y),( z, z+x,x),( y, x,x+y)|=4\ x y z
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Show that | (-a(b^2 + c^2 - a^2), 2b^3, 2c^3), (2a^3, -b(c^2 + a...
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Prove: |(1+a,1, 1),( 1, 1+a, 1),(1, 1, 1+a)|=a^3 +3a^2
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Prove: |(2y, y-z-x,2y),(2z,2z, z-x-y),( x-y-z,2x,2x)|=(x+y+z)^3
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show that |[y+z ,x, y],[ z+x, z, x],[x+y, y ,z]|=(x+y+z)(x-z)^2
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Using properties of determinants, prove that |(a+x, y, z),(x, a+y, z)...
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Prove: |a^3 2a b^3 2b c^3 2c|=2(a-b)(b-c)...
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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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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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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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If a ,\ b ,\ c are real numbers such that |(b+c,c+a ,a+b),( c+a,a+b,...
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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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Show that x=2 is a root of the equation |(x,-6,-1),( 2,-3x,x-3),(-3,...
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Solve the following determinant equation: |[x+a, b, c], [c, x+b, a],...
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