Without expanding the determinant, prove that `|(a,a^2,bc),(b,b^2,ca),(c,c^2,ab)|=|(1,a^2,a^3),(...

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Without expanding the determinant, prove that |[ a a^2 b c; b b^2 c a; c c^2 a b ]|=|[ 1 ... Without expanding the determinant, prove that |[ a a^2 b c; b b^2 c a; c c^2 a b ]|=|[ 1 ...
|[ 1 a a^2-bc; 1 b b^2-ca; 1 c c^2-ab ]|= (A) 0 (B) ∑ a^2(b-c... |[ 1 a a^2-bc; 1 b b^2-ca; 1 c c^2-ab ]|= (A) 0 (B) ∑ a^2(b-c...
By using properties of determinants, show that: (i) |[ 1 a a^2; 1 b b^2; 1 c c^2 ]|=(... By using properties of determinants, show that: (i) |[ 1 a a^2; 1 b b^2; 1 c c^2 ]|=(...
By using properties of determinants, show that: |[ a^2+1 a b a c; a b b^2+1 b c; c a ... By using properties of determinants, show that: |[ a^2+1 a b a c; a b b^2+1 b c; c a ...
Prove that |[ b+c c b; c c+a a; b a a+b ]|=4 a b c . D Prove that |[ b+c c b; c c+a a; b a a+b ]|=4 a b c . D