Show that `|(3a,-a+b,-a+c),(-b+a,3b,-b+c),(-c+a,-c+b,3c)|=3(a+b+c)(ab+bc+ca)`

Using properties of determinants, prove that |[3a,-a+b,-a+c],[-b+a,3b,-b+c],[-c+a,-c+b,3c]| = 3(a+b+c)(ab+bc+ca)

Show that |(a,b-c,c+b),(a+c,b,c-a),(a-b,b+a,c)|=(a+b+c)(a^(2)+b^(2)+c^(2))

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

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

Prove that Prove that Delta=|(1,1,1),(a,b,c),(bc+a^(2),ac+b^(2),ab+c^(2))|=2(a-b)(b-c)(c-a)

The value of the determinant |(bc,ac,ab),(a,b,c),(a^(3),b^(3),c^(3))| is a)(a + b + c) b)a + b + c -ab c) (a^(2) - b^(2))(b^(2) - c^(2)) (c^(2) - a^(2)) d) a^2+b^2+c^2

If |(b+c,c+a,a+b),(a+b,b+c,c+a),(c+a,a+b,b+c)|=k|(a,b,c),(c,a,b),(b,c,a)| then the value of k is

Determinant Delta=|(a^(2)+x,ab,ac),(ab,b^(2)+x,bc),(ac,bc,c^(2)+x)| is divisible by a)abc b) x^(2) c) x^(3) d)None of these

Show that abs [[1,a,bc],[1,b,ac],[1,c,ab]]=(a-b)(b-c)(c-a)

Show that Delta=abs[[-a^2,ab,ac],[ba,-b^2,bc],[ac,bc,-c^2]]=4a^2b^2c^2